However, it just doesn't look good on some avatars. Is there no way around this for people with alpha-transparency in their avatars?
Hum I think this would indeed be problematic for some user.
If I may try a suggestion, maybe we should change the background colour of the usercard (instead of adding a shadow) for people with profiles?
I agree it should indeed be changed. It's a minor detail, but "breaks" the elegance of many users' avatars.
Personally I now avoid getting a description precisely because of that :(
Just look at the top users here on meta: Jeff, Bill the Lizard, Robert Harvey, Popular Demand, and many more, all have avatars with white or transparent background which are sort of "broken" by this change.