If you can make peer-to-peer transactions with it, then the coin operators are definitely not complying with Know Your Customer and Anti-Money Laundering laws. This will pretty reliably get the US Feds to raid your offices, seize your website and servers, arrest the principles responsible, and prosecute them. See also: Liberty Reserve.
On the other hand, if you can't make peer-to-peer transactions with it, it's basically a "blockchain" in name only. There's little advantage over traditional bank account systems. Maybe the programmability and verifiability helps? I just don't see that sort of thing doing a lot compared to the whole money-laundering use case, though.