It's really not, though. It's just associated with something that "seems greedy". I could argue that "nothing useful is done with the computational power used

It's really not, though. It's just associated with something that "seems greedy". I could argue that "nothing useful is done with the computational power used for playing video games or watching and producing films." I could argue that, but I think that line of reasoning suffers the same way yours does. It requires a value judgment and you think that the cryptocoin eco system has no value. Cryptocoins have tremendous value for remittances alone. We can argue whether it's optimal allocation of resources and I think that is a healthy debate. Mining is required for trustless, decentralized currencies with provably equitable distribution. But we could probably forfeit some of the latter and eliminate the proof-of-work entirely (in fact it's already been done). Another option is to make the proof-of-work of greater independent utility from the transaction itself (also has been done).