Except it pays the wrong people. In Bitcoin, at least, miners are kept honest by other people running nodes that limit what miners can do. In this protocol the validation would become very expensive but only the miners are paid. This sounds like trouble.
No, the mine pool operator has to, but no more than once to cover every miner in his pool. To draw a comparison to bitcoin, there might only be a dozen or so pool entities which receive nearly all of the subsidy and transaction fees, but thousands of non-mining full nodes.