for me, the most valuable part of planning poker is when we see one vote that's way out of line with the rest, and that person explains their thinking, and some important discussion can take place. with asynchronous voting, i would imagine you'd get a fair bit of "oh, yeah, to be honest i don't remember why i gave that one an XL".
to be honest, i don't even see the point of keeping votes anonymous. if there's enough judgement in the room that people are ashamed to honestly say how difficult a task would be for them, i think that's a larger problem.