Sounds sort of similar to 0xbitcoin in that it's possible for anyone to mine tokens, but that project currently raises the difficulty (like Bitcoin). I'm assuming that a few changes to the difficulty scaling could make a proof-of-concept of sorts as a mineable ERC20 token. In this case, the security of the system relies on the security of the Ethereum network though, which shifts the concerns but also means that people still need gas to send transactions - which might be difficult for user adoption.