I mean, one of the best Pokemon games was Pokemon Snap. I think the series could and does have success outside of its core gameplay loop. So for me, a Pokemon of the Wild represents an open-world spinoff. And I think that could be highly successful. Also, having the game be a spinoff frees us from necessarily having all seven hundred and something Pokemon, which vastly reduces asset requirements to "whatever would work for this game."
I've actually been hearing about open-world Pokemon game ideas since, of all games, Phantom Pain came out-- 'cos of D-Dog. The gameplay loop of that game involved completing missions in an open world while also capturing guards for your base where you navigate the environment with a companion whose actions you can bring up via radial wheel in real time. In a similar way, an open-world Pokemon game would then lean on the same ideas-- complete missions in an open world while capturing Pokemon who can then become new companions for you to bring on missions whose actions are selectable in real time. But you gotta tweak the formula a LOT. Fittingly for the title of the thread, I think Breath of the Wild provides some of the missing pieces that turn the idea from half-baked into workable.
There are of course challenges. For one, Phantom Pain is good but it also kinda sucks due to its own open world. In this case, a smaller and more compact open world would probably be better. Secondly, in PP you are still the primary mover-- you move around, you fight, you shoot. In a Pokemon game, I'd suspect having your Pokemon NOT be the primary mover would be a bad thing. So you'd have this scenario where a character you don't have primary control over is your primary means of interacting with the world. This brings with it major concerns about things like enemies-- would wild Pokemon target you or your Pokemon? How about a villainous team? In an open-world scenario it's easy to abstract these questions away; you're standing behind your Pokemon who is simultaneously protecting you and attacking the enemy. A real-time or open-world scenario actually brings these questions to the fore. You start asking design questions like "should my character have their own health bar?" In this sense I can understand why people would instead prefer for the combat to be turn-based. It's a vast simplifier even if I feel it's limiting the promise of the idea, but I still feel like a commitment to a real-time paradigm could pay dividends when freed from the requirement to include all the Pokemon and do moves for all of them.
I feel like the main draw of an open-world Pokemon game, though, is the idea of being able to see Pokemon interact with the environment. People want to see Pokemon actually dynamically living in an environment when they say they want an open world Pokemon game-- they want interactions and maybe even an ecosystem. They want those moments from the anime where you got to see Butterfree flying in the air and migrating, or a Nidoqueen hanging out with her Nidorans. Similarly, I think people likely see potential for Pokemon-assisted physics-based sandbox play and world traversal. Stuff like solving puzzles at a power station by using your electrical Pokemon to power generators, or using a Fire-type Pokemon to cook food, or finding buried treasure with your Ground-type Pokemon. Exploring the ocean with your Water type Pokemon by Surfing or Diving. A move from the top-down perspective to something like third person might also capture the intensity of riding on a speedy Pokemon, or the rush of flying on the back of one.
So, what sorts of stories and settings accommodate these gameplay scenarios? Well, if we want a spinoff series, and we don't want all seven hundred plus Pokemon, we probably don't want the usual preteen trainer story. We don't want them to be the primary mover, so someone with a civilian-type role is probably preferable as opposed to, say, like, a cop or whatever Lieutenant Surge's deal is. We could go with a Pokemon Ranger, or we could go with a photographer-type like in Snap. Either works, and either gives us an out to de-emphasize combat over the main series. Our ranger could be focused on helping people and Pokemon who need rescue, while our photographer could be focused on exploring and documenting an island they washed up on. Just like in Breath of the Wild, moment-to-moment gameplay could favor exploration and traversal over combat, and gameplay would heavily feature both observing Pokemon interacting with the world as well as using your Pokemon to interact with the world. Another innovation from Breath of the Wild would be a consistent framework of physics rules-- stuff like conducting electricity with metal, or making wood burn. This would give typed moves all sorts of sandboxy interactions and could assist with the aforementioned puzzles. Using this as your framework for the gameplay loop gives you an excuse to effectively reduce the goal of the game to a secondary concern much like it was in Breath of the Wild. Have some quests, set an arbitrary goal for players to work towards, and little else matters. A ranger game could involve having a bunch of active distress calls after a natural disaster, while a photographer could just have washed up on an uninhabited island and have to explore to find a way back home.
Ultimately, I think that people who want a mainline Pokemon game to focus on the open world experience are limiting themselves by technical constraints and the demands of mainline fans. Thinking about "Pokemon of the Wild" as a spinoff series lets you think wayyyyyy outside the box, and I think that lets you frame an argument and construct a sketch for a compelling experience that stays compelling moment to moment.