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.
Doesn't this ignore the real world realities of economies of scale though with the physical materials being used? I'd enjoy a bit deeper explanation for this if you don't mind. :)
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.
It also has to make the networking part of Bitcoin fit within physics. From eyeballing the difficulty graph it looks like if you fixed the network difficulty in January 2010 then a new block would be mined every few picoseconds at the peak hash rate this year.
In the case of a fork in the chain the network decides the winner based on which fork ends up being longer. If blocks are being mined too quickly then forks become more likely and the state of the chain is more volatile as the current "winner" keeps flipping around.
Blocks being mined too slowly is a more obvious problem: less transaction throughput.
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.