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.

A key component of the hash algorithm used by blockchain is that difficulty can be adjusted, such that the algorithm ensures that the difficulty to mine the next block increases/decreases based on how long it took previous blocks to mine. In this way the network can attempt to maintain a predictable rate of blocks being mined as mining power fluctuates.

So for this to be a good computation for a blockchain to use it would have to have a way to modify difficulty in a predictable way.