Duplication of resources mainly. Bloat upon bloat. Worse, a Flatpak can ignore things that it probably should use on the system, and I'm not sure that's a good thing.
Don't get me wrong, there are supposed "bare metal" installs that duplicate all sorts of things too, and I don't like it when that happens either. Steam, for example, keeps at least one extra copy of itself as well as a bunch of other things.
And there's that Flatpaks an entirely different ecosystem that require their own set of updates.
I get it. I understand there are benefits. Doesn't mean I like it.