Because there will be the previous character's story, companions, NPCs, nemesis, etc...it's not a fresh start. I doubt the new character will even be from Tevinter. The only thing they're switching is the protagonist which is unappealing to me and makes no sense. Remember how at the end of the Empire Strikes Back Luke got closure and his story was done so it was only logical that a new random person joins Lando, Han, and Leia instead as the protagonist of RotJ and new random Joe defeated Vader and Luke just retired into obscurity, possibly giving random Joe some advice? Me either.
Star Wars is a trilogy with the same characters and one single plotline running through all three movies. It's not a good comparison to Dragon Age. You'd have a better comparison with something like Dune, where the first major plotline is resolved at the end of the first book. Book 2 begins to add new plotlines, and Book 3 introduces a new protagonist. Book 5 then introduces a new protagonist.
Additionally, nothing suggests the Inquisitor is retiring into obscurity. Quite the opposite, in fact: Trespasser shows they are actively pursuing Solas to stop him. I don't agree with your implication that if the Inquisitor isn't the PC then nothing they do can be important and they cease to be Solas's rival. So long as we're guessing, I'd be willing to make a bet that Solas will not be the front-and-center antagonist of DA4. He'll be in the shadows, manipulating events and possibly backing the main antagonist...just like the Inquisitor with the DA4 PC. What Inquisition and Trespasser have done is compelling: they've established the high-stakes conflict through Solas and the Inquisitor, and now they can keep evolving that and tying it in to whatever local conflict they are focusing on for a given game.