No, it doesn't. Transaction processors are paid by the proceeds from mining. That only lasts until the bitcoin cap is reached. Then they will start charging to process the blockchain.
Of course it's not solving the exact same problem (e.g. fraud protection), but it does seem like a basis for payment services which can.
Proof of Work is the innovation that solves the distributed consensus problem. It’s a feature not a bug.
Transaction processors are paid by the proceeds from mining