The problem that comes to mind is that the site is required to grow in accounts in order to continue functioning. In the long term, you'd need to add additional sources of revenue.
Also why would the first users join? The site would be dead.
Naturally the site owner would have a few hundred sock puppets they talk to themselves with, in order to bootstrap the social network. Growth hacking 101.
Exactly what Reddit did according to Huffman in the Coinbase talk.