It seems to me that voxel worlds could make this problem easier, not harder: you can deform the world algorithmically, voxel by voxel, rather than using polygonal approximations. Imagine an acid blob eating an outdoor environment in a fantasy game: in a voxel world, this is like a fancy seed fill. In a polygonal world, this is much harder to simulate.

I'm not saying voxel worlds solve every such problem; just that there are likely to be as many things that are easier w.r.t. animating elements as there are things that will be harder.

[Edit: maybe I'm not explaining this well, but I guess what I'm saying is that I don't see any reason why any voxels in a voxel world have to be static. The data structures don't force that; in contrast, in a voxel world with a clever data spatial structure, every single voxel can be a dynamic, particulate object, subject to computing power. As I argue above, though, this is not practical until computing power improves enough. Perhaps this is your fundamental point, in which case we're in violent agreement.]