I think it's easy to pull apart a game like this, and many of your solutions come down to 'do this area of the game better'. Do you not think the developer would not have wanted better designed puzzles if they had the choice? Do you not think they would not have wanted the shrines to be more aesthetically varied, given the choice?
There are some points that I agree with, but I think in general your post lacks consideration for why the design is the way it is, and in many cases the solutions you provide are not easily actionable. I've broken down the post below. I've removed the solutions for brevity.
Complaint: The game has 0 progression. I get why they wanted this so that you could go "anywhere at anytime" but it severely harms the pacing of the game and I feel much the same way at the end of the game as I do in the beginning (Minus the bigger stamina bar). Don't give me all the tools in the beginning, let me "earn" something.
Complaint: No meaningful rewards from side quests
It's certainly true that the game is not that rewarding, but they focused their time into the systemic design of the world. So, less would have been placed on adding lots of mechanics and features that have to layer into that systemic design. By focusing only on the core features they can make every mechanic interact with the world in a multitude of different ways.
I think the risk in unlocking new abilities and powers is that the game may not feel as good, until you unlock those. Take something like Rage 2, where the guns are locked behind vaults, dotted around the world. While in principle it seems like a rewarding way to get people to explore the environment, the reality is that without all of those guns, the gunplay is a little dull, and the game is just more fun, moment to moment when players have all of them available.
So the approach in Rage 2 actually backfires, because players only get the best experience out of the game, after completing most of it. Still, perhaps there's probably a balance that you can strike that helps players feel more rewarded than Breath of the Wild, but still gives players all the tools they need to have a good time without feeling forced to get to a specific place so that the game really opens up. That's a difficult balance to strike in a game like this, though.
If you consider other open world, fairly open ended games like Assassins Creed Odyssey, they don't have much for the player to attain either. Other than the progression embedded within the players skill tree and fairly arbitrary power increases (armour increases in strength but so too do enemies increase in their defense), everything is aesthetic. Perhaps a future Breath of the Wild game could have more cosmetics, or at least more variety. Dark Souls has a good approach to things like weapon variety (with a tonne of weapons in the games, but none of them are necessarily stronger, or replace what you begin with, they just provide more choice).
In any case, there's a lot of approaches they might take to this, but it's up to the designers to make the right decision here. It's also worth bearing in mind that there's a lot of merit to the sheer number of options you have available to you right out of the gate. While the world may not seem rewarding, it is very flexible as a result of all of those abilities granted to you very early on.
Complaint: Breakable weapons make combat pointless, when you get to the point that you have the best weapons in the game, engaging in combat negatively effects you.
There are many issues with the weapon system, they make combat pointless as you say (though this may be the point, without an explicit reward (e.g. combat to get past someone, to obtain a chest), then combat is a waste of resources. This makes you evaluate whether you should fight, or flee.
I agree though, that there's a lot of odd design with the weapon system. For one, it becomes pointless to open said chest when you already have a vast inventory of weapons, and because the only meaningful rewards are shrine rewards (stamina/health) you know that you'll never get anything meaningful, from the overworld. In that sense, everything in the overworld can feel a little pointless.
Consuming weapons and arrows only to open a chest to find a weapon which will later be consumed, doesn't feel very rewarding. So in this sense I think they would do well to look at the overworld gameplay loop and reward structure. Perhaps rupees could be more meaningful in the economy, and push you to delve deeper and deeper for treasure that you could bring back to camp? Perhaps rebuilding one of the villages in a significant way could push the player to find rupees. This is just a hypothetical suggestion, it doesn't have to be as I describe, but reviewing how the player is rewarded outside of shrines would be a good way forward.
As for weapon durability, I do think the idea that the durability means that fights come with a cost, creates a problem for the design. But it's important to pull back and look at the system and what experiential goal it's trying to achieve, before criticising or redesigning it. The durability system seemingly exists to encourage players to experiment, but at present the cost and abundance of breakable weapons likely stifles experimentation, as players either, choose not to fight altogether, or just cycle through a selection of the same breakable weapons to force their way through a fight. Neither of those options see players engaging with the world in fun or creative ways.
I think an answer to this problem probably lies in other games with disposable weapons / mechanics, like Spelunky. For instance in Spelunky, the player always has their default weapon (the whip, and jump attack) but the player can also find a tonne of different weapons which have value because they are powerful. In Spelunky a skeleton's skull is a one-use weapon (shattering when thrown) but offers considerable value because it enables the player to do things, that they couldn't otherwise do.
I think similar to that design, Breath of the Wild might benefit from allowing the player to attack freely (i.e. with a weapon with infinite durability) but then offering more situational tools in the environment that offer very particular value that extends beyond that default capability. This might be something like the wands which can set things alight or freeze enemies, or it could be a giant spear that allows link to charge large enemies down. Weapon durability could still feature, but having durability tied to weapons that all have roughly the same basic functionality doesn't help with variety at all.
Complaint: I hate the shrines. They are repetitive, They all have the exact same same visual design, with the exact same music, and many of them have poor puzzle design. They also only use the same toolset throughout the whole game.
Complaint: I hate the repetitive dungeon designs.
This is a big one where I think your suggestion is a little redundant. There are a million and one ways in which the developer could spice up the shrines, and make them more varied, but they all come with a fairly hefty development cost. They had 100+ of these Shrines to design, to minimising the aesthetic workload probably benefited the team significantly in getting all of this done.
Nonetheless, for future games I do hope more aesthetic variety is something that they consider. There are a lot of means in which they could interject that. It could be, as you say themed around the area its in, or it could be something else. Personally I like the idea that shrines could contain aesthetics and styles from a civilization that did not exist in the world above, and that they let you learn about civilisations, before those? I feel that would make sense as they are supposed to be ancient places. But, that's just one of hundreds of ideas that Nintendo could use to make the shrines more visually interesting.
As for the puzzle designs, yes, bad puzzles are bad. In order to get past that Nintendo would need to put more faith in user research and things like playtesting. As is, I don't think Nintendo do much real playtesting, and actually started doing this with Breath of the Wild. Still, I would imagine many of the puzzles relied upon the more oldschool design method at Nintendo, where they simply put faith in the designers to make engaging content that players will enjoy, and then hope that actually happens.
You can see that in some of puzzles. There's a disconnection between how you can see a puzzle being experienced in a designers mind, and how it's actually experienced. The ball gyro puzzle is a good example of this. I can see that, someone who's experienced with the gyro controls and enjoys using them, would imagine players having a lot of fun with this puzzle. But when it sits inside the context of the whole play experience, a sudden gyro puzzle with rather strict requirements for precision just ends up being frustrating. So the solution to this issue perhaps lies within better user research processes, which is going to be an ongoing change you see from Nintendo in the next 20 plus years (at present, they are not very mature in this department).
It's also worth noting that it's likely that while they experimented with this new open ended structure they may have wanted to keep the detail in the shrines and dungeons fairly minimal. It's possible that during development Nintendo did not know where the shrines would fit, or what the game would look like. The abstract nature of the shrines allows a developer to work on these without great consideration to the world above, which might be appreciable as it allows people to work more independently. Worrying about the context above and what aesthetic and puzzles should feature makes sense, but it might have been a burden that the developer did not want while they experimented with this new structure for the series.
Complaint: Navigating the world is honestly really... lonely.
I think this was a design choice. I think an alternative could be to have a companion that generally only speaks when requested, something subtle (like Navi from Ocarina of Time), but not imposing. Someone that can be present to speak to when requested, but won't interrupt the sense of isolation. I think that your suggestion of having someone like Zelda to tag along with would really spoil the deliberate tone of the game.
And even though I suggested having someone like Navi to accompany you here, it's really not required. I'd prefer it personally, but it's a very subjective thing and for some the game will offer a better experience without any companionship at all.
Complaint: The story sucks, most interesting bits are told during flashbacks. Each areas story is just copied and pasted between different areas.
The minimal approach to the story telling is obviously a stylistic choice, as for whether the story content is well written / engaging that's very subjective, but I can't imagine Nintendo were trying to make it bad, or uninteresting. It's likely that Nintendo wanted the story to be free-form (so players could approach it from any angle) and the most cost effective means of making this happen was just to make it very simplistic. Telling the same story 4 times is an easy means of ensuring that no player gets a drastically different experience regardless of the direction they choose to go, but I agree that it's a bit disappointing if you were hoping to be motivated forward by the narrative. Better and more diverse writing for each area would help here, but I think the narrative could also benefit by being much more spread out into the world (more NPCs, more quests, and whatnot to give the world more character).
Of course, all of this ultimately just comes down to resource limitations. If Nintendo want to spend more time on the narrative then I'm sure they will allocate the development resources appropriately. Breath of the Wild had its focus in other areas, likely because they wanted to nail that more innovative free-flowing structure before worrying about things like the narrative. By stripping it back it enabled them to play with the games structure without worry. Hopefully now that they've had practice at this more open-ended structure, we can see them bring back more narrative detail and depth.
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Just some closing thoughts. For me most of these were really non-issues, I personally only really take issue with the durability system and rewards embedded into the core gameplay loop. I think had the durability system been more interesting (i.e. weapons be breakable but had value that justified their dispensability, then the game would have been much more compelling for me. Equally, I'd like better rewards than just another breakable weapon embedded into the overworld (and even the bonus chests within shrines).
The rest, the aesthetic diversity, the narrative, the puzzle variety. Those are all fair criticisms but likely design choices that resulted from the already heavy development workload of this new approach to the Zelda formula. It's likely that this style would naturally become richer in those areas in future games.
