That's incorrect. The busywork is to prove that a certain amount of time is likely to have elapsed, as a coordination mechanism in a network of unreliable, uncoordinated, or even adversarial actors.

PoW is valued by the network and its participants.

What needs to be accounted for are the carbon and other negative externalities dumped into our singular shared environment. This is a massive global problem that you do a disservice by focusing on PoW.