I think the only reason for Proof of Work is to make it seem like "mining" is some expensive activity. But it doesn't have to be. It's a bit silly, actually.
In practice, PoW just winds up "electing" the next miner who you hope will compile all the transactions they see into a block. That's a single point of failure, they can charge inordinate fees, they can be DDoSed, and so on.