Bioware painted themselves into such a corner, it's frustrating.
I think the biggest thing is that "Mass Effect" could have and should have been bigger than Shepard's journey, yet Shepard's choices at the end of ME3 so radically change the galaxy that it makes any future games near-impossible to follow-up without either picking a default ending or radically retconning what occurs.
Andromeda had the right idea flash-forwarding hundreds of years into a totally new galaxy... but the execution was so bad and the potential so squandered (and Andromeda itself is widely regarded as a meme of bugs and unpolished design, fair or not) that even that future, while still the most limitless, is tainted in the public's view.
There are at least 6 options I could consider, all depending on execution.
1. Direct Sequel - if you're going to do a Mass Effect sequel then I'd bite the bullet and just pick a canon ending. Dragon Age has countless endings that have major story characters possibly die, but Bioware still made sure there was a "canon" path forward. Even if Leliana died in my playthrough, she's going to be in Inquisition, etc. While "Destroy" is the only option that permits Shepard to live, it still does so at the expense of the Geth and EDI (something something bad Starchild logic, etc.). I honestly would create a "fourth-path" pick-up option that cherry-picks from all three endings to spring from. Some things would remain consistent (the Mass Relays needing to be rebuilt, the Reapers either destroyed or returned to Dark Space) while others just probably shouldn't go forward (Synthesis remains not just a psychological and physiological nightmare scenario, but it's pretty high up there in terms of body horror for me too, and I doubt anyone would want a sequel where everyone was a glowing green flesh-borg hive mind collective....). "Control" might actually be the ending that does the "least harm" to the Mass Effect status quo, even if it's not the ending I would ever pick. But, granted, no Shepard if that happens.
2. Andromeda 2 - Yes, Andromeda was a disappointment (and I played it long after the patches). It has so many annoying flaws, bad writing, unpolished missions and cutscenes, and it definitely wastes its initial pitch to such an embarrassing degree it's frustrating. But... that potential was so limitless that I would still like them to try again. They kind of screwed up a lot of big moments (first contact is embarrassing, the lack of new aliens is shocking, the main villains are bland, etc.), but Andromeda is a big galaxy and you could technically argue that we only explored less than 1% of it. There could be hundreds of other alien species out there, more exotic planets, more interesting alien races and cultures... a second change to do what Andromeda promised us and really nail it. But it would have an uphill battle after the last one was so poorly received. It has the most potential, but the least public support, I think.
3. Mass Effect prequel - The First-Contact Turian War was a major event in human history that was full of conflict, misunderstanding, and generational bitterness that lasted several decades that was barely explored in the main games. It's a good setting for a Mass Effect game, one that avoids the pitfalls of ME3's ending, but one that is also limited by knowing that the status quo of ME1 must be in place by its conclusion. Still, the nuances of how the war started versus how it concluded could vary widely in the hands of a good story crafter, but it also runs the risk of undermining the alien-human relationships that Shepard's journey focused on mending.
4. Mass Effect Reboot - the setting and lore is all there, and if you were to just "start over" at a blank slate around the ME1 era and just ignore the Reaper threat, you could have a Star Trek-esque universe full of fascinating stories to tell that aren't marching towards the dead-end of ME3's ending. You could tell any story of any heroes or any villains, all against the backdrop of Turians, Salarians, Asari, Omega bars, Prothean ruins, Hanar brothels, Citadel hubs, and much more. However, it would have to entirely ignore everything in the ME trilogy and be, in effect, a full reboot - a new universe that only carries on the names and branding of the original Mass Effect universe, but not one hobbled by prior story limitations.
5. Mass Effect Trilogy Remaster - Just... do this. It's the one thing that would probably work best. There's a lot of rough patches in the original games that could be smoothed out and a lot of cut and bugged content that could be restored to make a re-release worth it.
6. Mass Effect Trilogy Remake - I would argue that it wouldn't be feasible to remake the whole trilogy from the ground up, the one thing a "remake" could theoretically do is keep 99% of the original games... but alter the endings to allow for future games. That's the sticking point to all of this, really, isn't it? How do you handle those endings? You either ignore them (Andromeda/reboot), predate them (prequel), settle on one (sequel), or keep them (remaster). But if you kept the journey the same and just... did a better ending... I honestly think it would open the whole franchise back up. Now, they ALREADY gave us the Extended Cut, but that wasn't a new ending, just longer ones that were more character-driven and emotionally resolute. But if they had the options to re-do it, with the goal of opening the door to future Mass Effect titles, then giving us the trilogy again but with a new ending (with maybe the original endings selectable as an option), would go a long way.