The type of user who uses public keys usually knows better than to use server-side key management on a social networking site (however pretty the interface may be.)
Oh definitely, that's why I highlighted the lack of innovation in browsers for handling keys and encryption/decryption. This all needs to happen locally (not the trendy thing these days) and the current tools aren't at the level where that's going to happen at a large scale.
There would still be the key-exchange problem (I can't imagine a system that would make it easy for non-technical people to exchange keys out of band, even if you could explain why that was necessary and what it means), but with good browser tools I bet the number of zero-knowledge type sites/p2p networks would explode.
I think if you take away the need to it to be really truly secure it's workable. Social profiles aren't nuclear secrets, they are just posts about topics and pictures. I think if you embed the private key with a symmetric key password that would be good enough. I do wonder why that hasn't been done especially in the era of native mobile apps.