You wouldn't play the game. So... Whas's the interest in all these threads?
I wouldn't play the game if it had either of those two crappy scenarios:
-The inquisitor dies offscreen between games and is never mentioned again like Emily Wong
-The loss of the hand is used as an excuse to show that the inquisitor is now a helpless invalid who can't fight at all and is relegated to the role of questgiver while some new and unrelated person finishes what I see as a very personal story between the Inquisitor and Solas.
I would definitely play it if the inquisitor was the protagonist again and the loss of the hand was given an emotional impact, he had to learn to overcome it and not only get by in day to day life but fight again.
Unlike the previous phrase which referred to themselves exclusively, the phrase you're saying could mean them saying that the Inquisition would save the world, not them. And they then say 'we'll find people he doesn't know' and points at Tevinter. The hints of a new setting and people are pretty obvious.
To me the "we'll find people Solas doesn't know" could easily point to new companions or a new military structure recruited from Tevinter. It would seem really odd for me if it meant "let's go all the way to Tevinter and find some random nobody off the street to take up the fight against Solas!" If they just needed a random person "Solas doesn't know" (I find that to be a horrible excuse anyway sine Solas is hardly a master strategist/manipulator and has proven unable to predict not only the outcome of his own actions but also the smallest things such as the inquisitor having a personality he likes, Cole being able to become human-like, and so on) then there's no need to go to Tevinter, just recruit some random new person from wherever you are and make sure they're not an elf.
I dunno. I imagine a powerful Knight-Enchanter would lose none of their powers in the event of losing a hand. One thing I always wondered though. In such a case, could a mage use something smaller to focus their magic instead of a staff? It worked for Harry Potter right? Inky would have to learn to wield the spectral blade with the right hand though.
I feel like mages in general wouldn't be affected in combat by the loss of an arm and other classes could learn to fight a bit differently and overcome the loss. Ex: a shield strapped to the arm with the severed hand, a dagger or hook attachment, that crossbow attachment from the Red Jenny epilogue, etc...
The contrast between what you say if you are going to keep the Inquisition going and what you say if you disband is confusing as well.
If you're keeping it "my adventuring days are over", if you disband "now excuse me as I have to save the world, again."
So I assume that if you are doing the former, then this is just to explain why you actually won't be hanging around Orlais doing the Divine's will but will have a deputy standing in for you, because officially you are retired from active service, but the reality is you are off chasing Solas. Whereas, there is no need to explain your absence if you disband, since no one expects you to stay.
That's my interpretation as well. It seems to point to that even more strongly since right after saying "my adventuring days are over" you're still there secretly plotting in the basement with your little anti-Solas group just like the "I guess I have to save the world...AGAIN" people. You're not like sitting in a rocking chair on a farm somewhere.
But would having the quiz as the protagonist for the next game be bad from a business perspective? Since that would kind of limit the potential to attract new people to the franchise?
When has a continued protagonist ever hurt sales? Look at the sales of ME1 vs ME3 or TW1 vs TW3, etc...If someone sees the series and thinks they would be interested in it, they'll either be more casual about it and not care about the history or they'll be happy that they have more content to play (the previous games in addition to the current game). Often people go in thinking like the first type but enjoy it so much they go back and get all the older games as well 
yeah that's my impression as well. If our quizzy's come back in DA4 though I'd suspect it'll be like in some form of advisory role much like Hawke did in DAI a;lthough I doubt they'll be in a fighting part like Hawke can
That's what I'm afraid of. 
I really HATE the idea that the loss of a hand would render someone who is this elite and almost godlike fighter utterly helpless. No possible way they could learn to use a simple prosthetic, focus on fighting with the other hand, work their way back up. I'm an artist, I draw quickly and skillfully with my right hand. If my right hand was severed do you think I would give up art? Would I just advise other people on art and not begin to learn to use my left hand to draw? Even using my left hand NOW, I'm leagues better than some beginner who doesn't draw because of my existing knowledge, skill, and technique. An elite warrior with one hand severed would be a better bet to save the world than a random former slave/merchant/noble/whatever who has little to no fighting skill or experience.