I've heard this a lot. I think there are two problems with this. First, you need massive adoption for the "social" part to be at all useful, hence only the few big social platforms can even try it. Second, even at maximum possible adoption, you'll probably run into the problem that actual human social networks have nowhere near enough branching breadth to help rank the behemoth that the web is today, i.e. for most queries and most possible hits, there's not enough signal coming from the social network.

The benefit of this approach is that it's an addition to PageRank, not a replacement. You don't need massive adoption of the social part I think cause you can link to eg HN, which already links to other sites. It's simply extending the backlinking concept to add personal pages.

Most long tail queries work well enough with Google and indeed most of the benefit of this approach would be in the head where ranking matters more. Furthermore nothing prohibits users from liking domains, not just individual URLs.