So, there is this bug report that is status-completed about transparent profile pictures not working, however it was 'fixed' by making the transparent background white. Then there is this bug report that has received no official attention at all and there is the comment by Oded ♦ on this answer in the recent new profile discussion that simply states that white backgrounds are here to stay. Everybody (read all the posts on the topic I could find) seems to agree it looks absolutely horrible on non-white backgrounds (for example on stackexchange.com itself, the top bar or sites like scifi.SE), so that statement did quite surprise me.
Now, from what I have read I could hypothesize that this is purely because imgur doesn't support resizing images with transparent backgrounds, however this sounds like an issue that StackExchange should be able to get fixed if they would try~ so I doubt that is the real reason.