What's lacking with the current animations? Just lame style?

I suppose that's one way of putting it. Your later comment on often not taking advantage of all joints is relevant - a lot of the main hero animations are rather stiff and unnatural.

The animations are better than a ton of other indie games. I see lots of games like this that look great in stills but look awful when moving.

I can't say I've seen much in the way of comparable indie games - most art I've seen is sideview, or, even if top-down, much more stylized, often hand-crafted pixel art. It doesn't really seem entirely relevant, though - if it looks good or bad or whatever, then that's how it looks, regardless of what others have done.

But the amount of work to re-render everything is probably too high a cost at this point.

Too high a cost to whom? So far as I can tell, the only person it would cost for me to tweak some animations is myself.

Finally it's a question of how much detail is retained when rendering the heroes at ~60px tall. We don't expect these animations to e.g. work in 3D third person. They just need to look nice for the output sprites.

I'm not really sure what you're saying here, though I can confidently state that pixel resolution is a primary limiting factor in the quality of sprite animation. Honestly, two of my favorite games, from a visual perspective, are Diablo II and Starcraft, which are only moderately higher and indeed much lower, respectively, in terms of typical pixel size.

Some animations don't work (for heroes) at all with the current layer system. E.g. can't have a spinning attack because that required reordering layers per frame

I have to admit, that's not a limitation I had considered previously, though I don't expect it to be of much concern to me. The particular example of spinning is, I think, an overused thing and quite silly in many cases.

We can't really add more frames of animation if that's what you're considering. All the permutations for 8 directions, several animations, and all the equipment means the game already takes a considerable amount of memory. If we roll out the "hdcore" version with no new frames the game will require 1GB of video memory which is steep for such a simple 2D game. (actually more than my dev machine has).

I can state, rather less confidently than before, that I think temporal resolution is also not a primary limiting factor. Although attack animations are a much different case (shorter in Flare, and longer in Diablo II), e.g. running animations are the same number of frames in both games. (I've been staring at its animations frame-by-frame a lot in working on similar artwork unrelated to this thread)