If one thinks about it, a properly used social network also doesn't need proof-of-work, because it has social proof. If three people you trust have spent 2 years regularly liking posts from a fourth account you can be quite sure that fourth account is no fake.

Reasonably. Sybil attacks still happen with frequency.

I've also noted that creating a new account with little visible connection to another can also re-establish social connections fairly quickly. After getting booted off G+ at one point, (accessing the site via Tor), I decided to tweak the entire notion of a trusted identity (having already gone pseudonymous) by naming my new account "The Real Slim Shady". I managed to re-acquire most of my core 20-40 followers over a few days.

(Being able to corroborate the connection from other sites helped, though many people twigged on who TRSS was even before checking.)

I've also seen known users turn hostile in bad ways over time. Much as I've had the experience of knowing people who've ended up committing murder, or serious financial crimes. Vetting is a hard problem.