For me, personal connection is what make or break a story. A nation might be interesting but to me it's just a backdrop. I only care about it so much as I care about the individuals who are a part of it. When playing DA:O for example we could have witnessed a scene of Gwaren being destroyed and I would have cared a little in that automatic way you're like "oh no!" when you see something bad, but I wouldn't have really cared and I wouldn't have thought back on it. Meanwhile if there had been a scene with Ban Teagan getting stabbed through the heart I would have been infinitely more upset because this was a character I'd grown to know and like. On that note, "save the world" stories don't mean anything to me. It's the journey, the little details and the people you meet along the way that I care about.
If the game had been completely fresh with no Solas, no world ending crisis, and no inquisition then I would have loved to play a ringleader in a Tevinter slave uprising but that's not the hand BioWare dealt us. With things laid out the way they are, I want to play the inquisitor and have my revenge.
I agree with everything you're saying except for the conclusion it leads you to, that the Inquisitor needs to be the one to deal with Solas.
I would still want there to be a connection between Solas and the new protagonist. As I've said many times, I think they're fully capable of developing that relationship into something interesting. They've demonstrated the ability to do that before.
I think part of my problem is just the idea that the Inquisitor is the only one who could possibly have a personal stake in stopping Solas.
If they did it right you could even have a scene late in the game where the new protag confronts the Inquisitor, be it in the form of an NPC(preferably, in my opinion) or dual protag, about which of them has the more legitimate personal dispute with Solas, or they can call the Inquisitor out on being too personally involved while countless lives are at stake, or they can argue about how to deal with him with one arguing to save him and the other one punching that one in the face.
Of course the problem with that dynamic is if they're in perfect agreement on everything then what the hell is the point of there being two of them, which is why I'm against dual protagonists.
Anyway, another part of the problem is, like I said, Solas wants it. So, in my mind, if the Inquisitor beats Solas, whether by killing him or redeeming him, Solas wins, and I cannot allow that.