I've enjoyed skimming this thread as it is not an opinion I agree with, and I'd like to understand the other side of the argument. I was previously under the impression new game=new hero, but Trespasser really threw me. Who knows what they are planning. They may not even know yet. I would have wanted a new pc next game, but since Trespasser left my Lavellan hanging AGAIN... Thanks Patrick "The Troll" Weekes. 
So the Inquisitor returns in DA4 with new companions completely with also having new LIs along with having old LIs write them letters or something?
That'll go really well with the fanbase
I recall hearing some time back that a dev asked fans what they would think about a Dragon Age game with no LIs. I have no source...I'm just throwing it out there in case someone recalls hearing this also. Anyway...the whole LI thing isn't really an issue with a returning protagonist. Bioware handled it with Mass Effect (some of the romances better than others). You could keep up your romance from a previous game (letters and a cut scene or two) or start a new one for whatever reason.
I get it, though I've been known to throw out the arm loss argument at times. Not because I think it makes the Inquisitor an invalid, but because I think it was a very calculated move on Bioware's part to excuse the Inquisitor not being on the front line in the future.
The arm as a calculated move is a sick idea. Bioware is not that kind of company. Let's not forget the story the devs wrote. They Inquisitor would have died if Solas had not removed the anchor. The removal of the arm kept her/him alive. If they were sure they wanted Inky's story to end they should have let him/her die from the anchor or by being turned to stone by Elfy's "Big Magic" (note to say that like Elam from Hell on Wheels). I would have been ok with that.
I just hope they do what's best story-wise instead of sticking to a formula for the sake of not looking like hypocrites or caving to whichever fans scream the loudest.