Is it possible to make a cryptocurrency that does "real" work as its proof-of-work: work which is computationally intensive, but it solves some real life problems instead of "wasting" the energy?
The network pays the nodes that run infrastructure rather than miners or stakers. Cost-of-attack is generated by the same nodes, so paying for infrastructure does not defund consensus. Security scales with fee-throughput of the network, while fee-throughput pays for scalability.
It is, yes. Curiously though, making the work "useful" might actually harm the security of a block chain and make it more likely to suffer a 51% attack.
With a chain like Bitcoin's, if you want to perform a 51% attack, you would have to purchase a large amount of SHA-256 ASIC mining hardware. After the attack, public confidence would be shaken so severely that the market price would crash, and might never recover. So afterwards, the attacker is left with a pile of ASIC hardware that's nowhere near as valuable as before.
If the PoW algorithm were based on something more "useful", then after a 51% attack, the attacker would have a large amount of hardware that they could easily repurpose, so it would retain a lot of its previous value. That makes the total cost of the attack much lower.
https://saito.io/saito-whitepaper.pdf
The network pays the nodes that run infrastructure rather than miners or stakers. Cost-of-attack is generated by the same nodes, so paying for infrastructure does not defund consensus. Security scales with fee-throughput of the network, while fee-throughput pays for scalability.