I assume it's easier to calculate and submit micropayments with a cryptocurrency than to connect with a real bank and do them with real money. Plus peers can trust that they get the correct payment for the amount they contribute to the p2p network, especially if the payment is via a smart contract.
The one big advantage of blockchain I know of, is that a group of people can negotiate some sort of payment (e.g. I do X work I get Y coins), and once they agree, nobody can break the negotiation. So assuming everyone understands what they're doing, they will get automatically payed and nobody will run off with all the money (of course if people don't understand what they're doing, they can get scammed like the many many crypto scams we've seen so far).