Bittorrent handles the distribution of large files. It explicitly doesn't handle any of the social aspects of content removal, indexing of humans by name, social graphs, etc. Spam is not a question because there's no "push" of any kind, but people would want push notification for any FB replacement.

If you were to build a system for distributing "wall posts" in a bittorrent manner, it would probably end up looking a lot like USENET with a group per-person. (Long ago I knew a couple of people who did in fact have their own newsgroup in alt.) That would also replicate the problems of USENET, especially with regards to spam fighting.