I know this won't be a universally popular opinion, (and, believe me, I'm quite surprised to be writing this myself) but, following the events of Trespasser, and that beautifully melancholic final conversation between the inquisitor and Solas, I'm now eager to play as the inquisitor again in Dragon Age 4.
The fact that Solas is capable of killing the inquisitor but chooses to save her instead, despite knowing that she'll do everything within her power to stop him, really hit me emotionally. That moment illustrated just how much Solas respects the inquisitor (at least in my game), and it set the stage for the best kind of rivalry: one between friends on irreconcilably diverging paths, with a tragic and, no doubt, tearful conclusion. lol
Introduce a new protagonist to track down Solas and all of that beautiful subtext is lost. Solas becomes just another Big Bad who our disconnected hero has to put down in order to prevent the apocalypse.
P.S. I also think that the inquisitor will be a much more relatable hero now that he or she isn't a "special snowflake". There's no more magic mark, no more grand, holy crusade. The "inquisitor" -- depending on the ending you choose -- is now much more like Hawke: a seasoned fighter and leader working alongside a relatively small group of trusted allies and contacts.
P.P.S. Yes, I know the Quizzy lost a hand, but -- in the increasingly insane magical melting pot that is Thedas -- I'm sure there's a way to remedy that minor inconvenience. If magic can heal serious wounds like deep sword gouges to vital organs, and bring people back from the brink of death, then there's probably a mage or two out there with a knack for regrowing limbs.
Surely anything Hogwarts can do, Tevinter can, too. lol
Even though I generally like the idea of a new protagonist every game and really have/had no desire to see my Warden or Hawke ever again, I would actually very much like to play my Inquisitor again, but with a few caveats.
1 I would prefer that it be in the same engine and have basically the same aesthetic as DAI so he seems (and looks) like the same person.
2 Along with the above, I would really want some way to import my appearance.
3 I do not want the missing limb to be -- har-har -- hand-waived away.
Losing a limb is a traumatic experience and I think there is an unique opportunity to do something special with it as a story device. I DO NOT want there to be some magical prosthetic that remedies "that minor inconvenience."
But... despite wanting it and agreeing with most of your points, I think it would be difficult. Not only will most players clamor for the their LI to be brought back as well, but the hand thing does present some challenges.
As far as the story is concerned, the post-credit Trespasser scene strongly suggests that we're going to Tevinter at some point. Is it in the next game? Who can say? Even though the (non-disbanded) Inquisition has little to no power in Tevinter, the Inquisitor himself as a person would be a noteworthy figure. In contrast, an Inquisitor who disbanded is merely the former Inquisitor, and without the mark is no more noteworthy than your average mage, warrior, or rogue in that regard. In addition to that, the great division among classes and races in Tevinter would also present challenges and I think offer too many variables for the devs to take into account. And of course, if those variables aren't taken into account then players will complain that "choices didn't matter."
And too, I did like the idea that the Dragon Age franchise was different from Mass Effect in this regard. Dragon Age is the story of Thedas, not a single person. Of course, now that Patrick Weekes (coming from ME), is the lead writer, who knows what changes he will make, if any, to some of the things that were previously stated as unchanging. But, we still have Mike Laidlaw and Mark Darrah steering the ship, so they will make the final decision as to her final course.