We can and do, all the time. And all puzzles are a "waste of resources", really.
I'm not into crypto and I do think Bitcoin is stupid and wasteful, but I don't find it "sick" or all what upsetting that this kind of puzzle exists, though I think some smart contract-based Ethereum puzzles could be much more interesting, demanding solutions to more interesting problems that don't directly relate to the blockchain itself. Imagine a smart contract with a pot anybody can pay into that pays out to whoever could crack a particular previously unsolvable problem. Basically a public bounty. The only downside is that it has to be a problem that can be validated algorithmically.
I'm not into crypto and I do think Bitcoin is stupid and wasteful, but I don't find it "sick" or all what upsetting that this kind of puzzle exists, though I think some smart contract-based Ethereum puzzles could be much more interesting, demanding solutions to more interesting problems that don't directly relate to the blockchain itself. Imagine a smart contract with a pot anybody can pay into that pays out to whoever could crack a particular previously unsolvable problem. Basically a public bounty. The only downside is that it has to be a problem that can be validated algorithmically.