There is potential for that, but so far I think BG3 is failing to even hint at internal personal conflicts within the group. Thus far we only really have Lae'zel and Shadowheart having meaningful interactions with each other. Beyond that, there aren't actually interesting group dynamics unfolding, so nothing for later acts to build off of. Hopefully the full game changes that at least.
Also I came to a bit of a realization about the companions and people's reaction to them. I suspect that part of the reason for certain people's dislike of the companions is a matter of perspective. I think the people who dislike them the most don't see themselves as witnessing a story unfold from a distance. They come at it from a perspective of being a participant in the world, and so when they're faced with a bunch of characters they dislike, they take the same attitude they would in real life; not wanting to spend time that should be fun and enjoyable dealing with people they find unpleasant. @neprostoman, I think even your post hints at that divide, since you're talking about them in terms of the story they'll create, while I've seen people who dislike them talking in far more personal terms about their feelings and experiences, about who they want around them and want to go through the game with.
