The security properties of Proof of Work cryptocurrency are derived from the wastefulness. We want to be confident that everyone has the same cost when producing a block.

If the problems being solved are useful, they are potentially more useful to some parties than others, meaning some parties may have a lower cost to attack the blockchain, because it was computation they needed to spend money on anyway, might as well attack a blockchain while you are at it.

I can try to explain further if that's confusing.