But the problem that I and a lot of people had with DA2 was that it felt incomplete. The big, world-changing part of the story happened at the very end. And to a lesser extent, that's the same problem people are having with DAI. You can't just leave the conclusion of every game hanging. That's just terrible storytelling. DAO was great because it wrapped up its own story while giving you hints at something bigger, but not making them more compelling than the story being told. With Inquisition, the dangling plot thread is a great big anvil dropped on you in the last 5 minutes of the game, hinting at a story way more interesting than the one you just completed.
Plus, this particular plot thread has pretty strong connections to the Inquisitor specifically. Will they ever find out who Solas is? Will they have to confront him? What are his plans? What is the anchor really? What purpose does it serve? Why did Solas give his orb to Corypheus in the first place? What will the consequences of drinking/not drinking from the well be? What happened to Flemeth? If you answer pretty much any of these questions with a new protagonist then they lose almost all of their dramatic impact. Plonk some random guy down in front of Solas and tell him that he's trying to f*ck the world up, and that random guy isn't going to have any qualms about dealing with him. That just kills any drama they built up by having Solas as a friend and ally for an entire game. Same thing for the well and the elven gods. Some random new protagonist might care about the elven gods, maybe. Probably moreso if they're an elf. But the Inquisitor has a magical mark on their hand caused by the artifact of one of those gods. They went to an ancient elven temple where they learned of the existence of these gods. Thematically, it really needs to be the Inquisitor who continues this storyline. If they're able to do it via DLC, fine. But with the revelation that there won't be an expansion, I'm hoping they turn it into a fully-fledged game, wrap up the plots they started in the first arc of the series (wardens, elves, perhaps some stuff about dragons and the theirin bloodline, companion stuff). Then we can safely move away from the south for Dragon Age 4 and deal with something completely different.
... But DA2's story isn't incomplete, at least if you think it as the story of Kirkwall's downfall, or the story of the origins of the mage-templar war, or even the story of Hawke, the Champion of Kirkwall. And, as much as I enjoy the inclusion of Hawke in DA:I, I don't really agree that there were *that* many hanging plot-threads that needed to be tidied up (like the devs kinda implied). Sure, his/her addition was a welcome extra, but in the terms of plot... I don't really see how the inclusion of Hawke made that big of a difference (except underline how much of a guilt-wretched tragic hero s/he is, but the importance of that is a bit questionable, IMO, unless the devs where implying that the plot-important development was either his/her death or his/her trip to Weisshaupt).
And as to regards of Solas, you're making a lot of assumptions there. He left the Inquisition, and therefore whatever happends from now on doesn't really affect the Inquisition all that much. He was there to help (and to try to fix his mistake), which is now done. Same with the elven gods and the sentinels, even moreso. Their involvement was pretty brief and unplanned, and its not like they make any formal alliance that has any impact on the Inquisition.
I mean, this is kinda like saying that Hawke should've been the protagonist of DA:I, since it was his/her actions and the actions of his/her companions that started the mage-templar war AND freed Corypheus, which in turn made it possible for Cory to enact his plan. And while imagining my sarcastic Hawke as the head of the Inquisition and the aneurysms it would've given Cassandra and my advisors is absolutely hilarious, I really don't think that would've been a good fit. And it's not like the Inquisitor is "just a random guy" either, even though his/her part in the event that led to the Conclave are absolutely inconsequental, or lessen the dramatic impact of your choices, IMO.
But I guess this is something we'll just have to agree to disagree.