I must say, I do love that Winter Palace dancing scene. It's so sweet and cool and romantic. I really appreciated that BW put that scene in there for Quizzy and their LI. A great little detail that added alot of Heart.
Yeah, I adore it. 
Although it does cause some laughs for Solasmancers. When you ask him to dance, he says something like, "I doubt the Orlesian court would approve of you dancing with an elven apostate." It's like, "I am an elven apostate! Can't sink much lower than that." I totally headcanon that she was paraded around as a "tamed savage" much like the poor real-life Pocahontas was when she was taken to England.
Although, confession time: I haven't romanced Cullen with an independent playthrough. It takes too long, so I just used my Solasmance playthrough, cut it off to just before kissing him on the balcony (which locks you into the romance), and had her go play chess with Cullen instead for that romance playthrough. I want to make a new playthrough with a Surana worldstate (not Tabris worldstate like with Solas), but I can't see any Dalish Inquisitor of mine choosing an ex-Templar over a fellow "heathen" elf. I can only see her choosing Cullen if she went to the Winter Palace first, where she can see Solas' questionable morals in action (Mr. "I do adore the heady blend of power, intrigue, danger, and sex that permeates these events"
) and see that Cullen is a good and honest man who also detests the politics and backstabbing as much as she does. Doing so first means that I sacrifice getting to go to the Orlesian Ball as part of a couple with Cullen, though, which means no dance scene. 
I for one am in favor of a new PC for the next game. Especially if we're going to tevinter. I would like a PC that is from the area. Along with all new companions.
I'd personally be okay with a new PC only if the Inquisitor can return as, say, a significant NPC or co-protagonist, if just to return to help resolve the Solas situation. The ending to Trespasser set the Inquisitor up as someone who vowed to stop Solas, and their final scene is shown to be looking for allies to either put him down or save him from himself. I'd be really disappointed if that setup had no pay-off.
Plus, Solavellan fans want closure to the romance. 
I also feel like if we are having new PC's every game, then they should really cut down on the cameos and returning companions as new companions. It creates this weird shift, or split in me. On the one hand I'm this new PC, and don't know these characters. On the other hand, I'm the player and we've been through hell together. So, I'm happy to see them and they're like yeah, hey whatever.
I do not find it satisfying.
Me neither (MORRIGAN! It's me! The woman who loved you and arranged to help you conceive your child! How do you not recognize me?!), but I feel compelled point out that we've had new PCs every game except for DAA, and that hasn't stopped them from including tons of cameos and returning companions every game. In fact, DA2 had more returning companions and cameos than DAA, despite how DA2 had a new protagonist with Hawke whereas DAA had the returning Warden. 
That's actually part of why I want returning protagonists more new ones (although I know I'm outvoted on this). If they're going to keep bringing back old companions and allies anyway, I want the game to acknowledge our shared history instead of, as you said, that "weird shift" where I know who they are and I want to catch up on old times, but they don't know my character so they're like, "Who're you? Back up!"
(I'll be especially upset if they do this for Solas. They can't have slowly built up the Inquisitor's history and relationship with Solas, who slowly rose to power and became a world threat right under the Inquisitor's nose, just for some random stranger from Tevinter to be the one to face off against him and stop him.)
And I admit, I was a tad bit envious of Bull and his Chargers. They seemed really close, like a little family. That was the kind of feeling I got with DAO and DA2 companions; a small band of outcast, roving "mercenaries" that needed each other. I did not feel that with DAI. I didn't feel like they were really "with" me as much as we were collaborating on a project, but their real alliances and "family" were elsewhere.
I mean, I think they wanted the companions to be kind of big shots in their own right, and with "their own lives" and all that. Which is great on paper,b ut-for me-in game it made for a bit of a disconnect.
I agree. I loved the fire-forged friends aspect of previous DA games and missed it for DAI. Everyone in DAI is always so distant and professional. With only a few exceptions, if you don't romance them then most companions and advisers keep you at arm's length and constantly remind you, "You're the HERALD!" or "You're the boss." I think Dorian, Cassandra, and maybe Cullen are the only companions/advisers who really, truly embrace you as a friend and make you feel close to them even if you don't romance them. With everyone else (including Varric), it's like, "Good to see you, boss," or "All touched up, Lady Herald?"
I get the feeling they wanted to make the Inqusition seem like this big, professional, political organization, so they wanted companions/advisers to emphasize the professional relationship between the Inquisitor and Inquisition forces. (especially Cullen, Mr. Consumate Professional, even in a romance.
) But by having the companions and advisers constantly emphasize "You're the Herald/Inquisitor! I'm just your employee," if makes us feel so isolated and lonely. Maybe that's also what they're going for, since one running theme of the game is how the world idolizing you can make people forget you are and stop treating you like a person (as you can talk about this with companions and advisers all the time), but it sure is a lonely experience. Not trying to make a generalization about gamers, but many people in the modern world already feel lonely and isolated in real life; we don't want to feel that way playing a game.
For good or for ill, DAO and DA2 starts before the protagonist becomes famous, so you meet and connect with your companions as a regular person. Your companions knew you as the Warden or Hawke before you became "The Hero of Ferelden" or "The Champion of Kirkwall." For DAI, while it was a clever idea to have the game start with you becoming "The Herald of Andraste," and to have you meet most companions/advisers after you've become famous, it does prevent that emotional intimacy and close friendships allowed for DAO and DA2.
I wouldn't be sad if they skipped this for DA4. I want to feel close to my companions again, not an idol or a boss they keep at arm's length. 