After reading through, I find myself falling into both camps somewhat: the lack of being able to talk at any time was jarring, especially for the romances, but the increased interweaving of characters and their mission was a very good experiment. It's easy to forget how new this sort of 'epic RPG' genre is: there's no set formula for what will always work, and there may never be.
Two things that stood out to me as missing actually surprised me: epilogue investment, and the traditional duty of characters as walking lore-compendiums.
The first doesn't seem like much, since it's not voice work in and of itself, but one of the functions of the end-game epilogue slides was always to give us an idea of how our characters turned out. The differences between, say, hearing Alistair turned into a drunk, or a maleable king, or even a skilled ruler, were all pieces that not only gave closure, but also connection to the character. What we did, mattered.
Now, in some respects this seems implausible for DA2, for reasons that should be obvious: Varric is telling this story, and in the first fifteen minutes claims not to know where the Champion is. The ambiguity is a large part of the story. On the other hand, there still could have been 'epilogue rumor' slides: nothing too obvious, but also give some sense of direction. All in all, the Origins epilogue slides before you went to Awakening, if that makes any sense. The point being, the closure also brings the characters to being a bit more relevant: people like knowing how they affect the cast.
The second traditional role of a character, as a lore encyclopedia, might also have mitigated the feeling of being all hit-or-miss. That's a staple of characters like, say, Tali in Mass Effect 1: they have their personal stories, which are usually one at a time, but at the same time you could go back to them to re-hear exposition about their pasts, culture, etc. It's not particularly glamorous, but if you do it well, with slowly-expanding repeatable dialogue options (like Leliana's increasing number of stories), you both have progression and the ability to get dialogue at any time.
A case example of what might have been: let's take Anders.
In Act 1, Anders starts off with a basic 'who I am' repeatable dialogue list, or even the same one from when you first met him. He was/is a Warden, he dislikes the Circle, he had a cat. One past, one personal, one codex-worthy exposition on the Circle.
In Act 2, Anders can be spoken at any time for those same three prompts, but adds another two: you can ask Anders more about his time in the Wardens (giving both personal accounting and character inflection), and his insight from having been within the Circle Tower.
In Act 3, Anders gives another two to be accessed at any time: maybe something about apostate societies in general (giving us a nice codex about how they might be organized and run), and spirits with the veil.
In essence, these aren't anything that haven't been done, but rather making the codex-exposition pieces accessible at any time for later chatup and review. You might get much the same influence if you just took what they already told you in an arc (Fenrir's exposition about Tevinter, for example), and made it so that after you did their loyalty mission you could go back and pick up that Act's exposition.
It's something to do, and it can allow for some avoiding of the 'must memorize all investigation options the first/only time I see them' syndrome that I notice.
And just to throw out a third thing, you could throw in a 'spend time with your pal' dialogue/fade to black. Nothing fancy, even just a line, but reflective of your current state of relations: Rival, Friend, Neither, Love Interest. For love interests it might be your 'let's spend time together' fade to black, but everyone could have a basis for a platonic fade to black: Merril tells you about the Dalish, knock back a few beers with Isabella, play cards with Varric, brood with Fenrir...