OK here is a challenge for those Pro-New PC advocates out there.
Without using the concept "I want a clean break from previous games" or bringing in arguments why you do not want to the Inquisitor to return as a PC (I've stated why I disregard the Missing Arm, the Budget, and the "One PC Per Game" arguments at this point, they are easy excuses and all can be gotten around in a number of ways to facilitate a returning Inquisitor PC) give us reasons and story elements why you want a new PC. After all, arguing against something old does not innately support the benefits of having something new.
Because of some people giving these positives of what a New PC could bring to the story, I've found myself strongly on the dual PC crowd now (when I started I was hard core sole Inquisitor PC) and I do see the genuine merit of have a New PC (twice that level of merit if they come with the elusive "Insiders Perspective"). I know you guys have great reasons for this, I just wish you'd use them more. So rather than harping on the same tired 3 default excuses as to why you don't want a Quizzy PC again, give us your best shot on what you simply want to see from a New PC! What do you see as their story? What do you want them to be? 
It's alot more fun to debate potentials after all!
There have been many more reasons than those three, and also you not accepting those three reasons doesn't mean that you've convinced everyone else that they're invalid.
As others have said, if we have the same PC, the history and relationships with returning characters will be the same, which is stale. Calpernia is a good example, as an Inquisitor couldn't reasonably have anything other than an antagonistic relationship with her, at best a wary tentative truce. A new PC can have any kind of relationship with her.
To me, having the Inky as protag in Tevinter translates into one PC background, regardless of our race. Because we will play at the southern Thedas outsider working for a shadow organization dedicated to stopping Solas. This is the same if we're Qunari, mage Trevelyan, Solas-romanced Lavellan, chose to disband or remain as the Divine's honor guard. The Inquisitor-as-PC has the same role imported into DA4, so it would be like Hawke all over again. New PC allows for much more freedom of storytelling, multiple backgrounds, new view of Thedas and the nations the game will take place in.
And your argument goes both ways: there are any number of ways for Bioware to get around the pro-Inquisitor PC arguments, as well. We just don't know enough at this point to make any reasonable assumptions.
I just want to see ONE plausible way that Solas would care about the new PC and not simply kill him for getting in the way. Or ONE plausible situation in which the new PC could care about redeeming Solas and not just killing him as some big bad. Every new-PC scenario I've read so far involves Solas being dumb or acting out of character.
How about an infinite number of reasons how a new PC could interact with Solas? We have no idea what the plot of the next game is going to be, so Bioware could make any number of ways for a new PC to establish a rapport with Solas (positive or negative) and have a reason to work against his plans. It is futile to provide concrete examples at this point, since we don't know what is going to happen in the next game, other than (most likely) Tevinter and Qunari and Solas' plots.
If you asked me five years ago how I could conceivably have a non-Hawke protagonist deal with Corypheus, I can guarantee I would not have said "OK so there's this peace conference we're at, but it asplodes and we get stuck with a piece of the Fade in our hand, and it turns out Corypheus was behind this except it turns out Solas was really behind it except Solas is really the Dread Wolf and has been plotting this since before DAO"
I've said something to this effect before but..
I like making a new character, I like making multiple characters and seeing how that changes the story. I like the fact that each dragon age game has a new/multiple new protagonists, I love getting new backgrounds, perspectives, story, companions, and relationships. That's pretty much why I want a new protagonist, its not that I have any problem with the inquisitor, it's just that the returning of any protagonist would cause me to miss out on some of the things I love about this franchise.
As for what I might want specifically for Dragon Age 4 :
I want origins back, I want multiple different starting points that give my character a different identity, and show case a different part of Tevinter society.
I want to see a slave rebellions and the Qun conquer more vint territory because these are things that could vastly effect my character because this is their home and these things will change that home.
I want to see Calpernia again. Not as an old rival but as a slave freedom fighter and potential companion. And I want to see Lace Harding because she would be a good way of connecting us to the Solas plotline (if indeed there's going to be any/much of that plotline in DA4) and because I just like her.
And someone posted a thread a little while ago suggesting all origins start in the same city, doing different things, but are all in the end forced to defend their city from a qunari siege, only to flee with the main plot hook character when the qun wins - I love this idea.
Yes.
I would like it if Calpernia is a separate political faction to Dorian's, and perhaps we could choose to side with one or the other, or she provides some side quest chains. I don't know if I'd want her to work with Dorian and Mae, or keep with her more conservative military methods for reforming Tevinter. I like the idea of several groups dedicated to reform but using different methods, and having different ideas of what those reforms would be like. It could set up a good moral choice of Calpernia's group being staunchly anti-slavery but pro-magocracy while Dorian's group is focused more on equal rights for all citizens, mage and non-mage, but not addressing slavery, or not to as much of an extent as Calpernia would.
No offense, but that all sounds terrible. The only one that sounds sort of tolerable is the second. The first and fourth just sounds like Dragon Age: Origins 2.0, and the third involves an absolutely terrible person being a companion and Bioware doing the whole "morally grey is good" thing.
So you would rather than DAI:2 than DAO:2.