Well, we're just sharing opinions here, that's an assumption for you to think I care as opposed to how I view the next protagonist.
Missing an arm, most companions are either gone or dead, hang up with LI, the Inquisition itself is disbanded or not. That's enough variation they need to take into account for, and I would rather they start something new entirely which they have and I'm happy with it. They carry the world state over, so that it can be resolved in the next game, just as the mage and templar conflicted didn't get solved by Hawke, Solas will probably be dealt with by the next protagonist, at least, we'll see the Inquisitor cameo like with Hawke, and that should be enough. Bioware doesn't carry everything over, just the big decisions that can have an influence on the next game. The series is about Thedas, not about any singular hero, the setting and cliffhanger is for the Thedas world, not for any particular hero.
How would you say they are starting something "entirely new",if you don't mind my asking. To me that does not seem to be the case, though i would vastly prefer if that were the case. It is heavily implied at the end of Trespasser that the Inquisition will "recruit" those who will stop Solas. That is not, to me, "entirely new".
The idea of a cameo is a problem in itself. People did not like Hawke's cameo, so are apprehensive about how the Inquisitor will be handled.
And if the series was just about Thedas, should that not be enough for more games? Why, then, is there a need to carry over villains and hero's of years past? DA Origins to 2 did this very well. They were connected in the sense they were both a part of what was going on in Thedas, and we needed Hawke because the Warden was otherwise indisposed. But, because of the constant throw backs to Hawke in Inquisition, DA2 to Inquisition did not work as well. With Solas' story potentially being a fairly big part of DA4, there will be constant throw backs to them. And it seems the vast majority (people from every camp) believe that the Inquisitor should have a fairly big role in stopping Solas. They made the Inquisitor invested in Solas and his plans, love him or hate him. There is no option to be "neutral".
The end of DA2 left on a cliffhanger. But Hawke said nothing about stopping the Mage/Templar war. They did not get together with others and say "I'm going to stop this, no matter what". There was no cliffhanger for the character. The real issue with Hawke comes with the obvious places you stop and think "This was probably something Hawke was meant to do". As you said, the end of DA2 was a cliffhanger for Thedas. I cannot agree with you that the Inquisitor's end was not a cliffhanger for them. As PC or otherwise, the ending clearly shows the Inquisitor's hand (pun!) in future events is not yet done. That, then, is a cliffhanger for a character. Now if it had ended with Solas being dealt with and his story ending, the Inquisitor saying "we have finished everything we have set out to do, thank you and good day", with no scene in Haven. Hurrah! Cliffhanger for Thedas, new PC welcome. A story about Tevinter and the Qunari with no baggage with the Inquisitor, just a mention of their deeds every now and again. As it happens, that was not the case.
This is how i interpreted the way DA has been. These are the reasons i think a new PC every time simply isn't working, and why i think just saying "it's about Thedas" is not a good cover for why a new PC is "needed". I would be interested in how you got your opinion, which is clearly different from mine. If you don't mind explaining, that is.