The trouble is that the reason PoW protects the network is that the mined block is an input to the PoW function. This means that if an attacker wants to change

The trouble is that the reason PoW protects the network is that the mined block is an input to the PoW function. This means that if an attacker wants to change the network it needs to spend the same amount of processing power mining another block (and as the blocks are generated, it's gets harder and harder to catch up) Can you think about a real world problem that also has the freshly mined block as an input? Perhaps we can have a randomized problem like a monte carlo algorithm of protein folding where the random seed is set by the hash of the mined block. Or something.