There are plenty of zksnark based crypto solutions out there that are both private and environmentally friendly. Bitcoin uses a particularly nasty and wasteful consensus algorithm that just happened to have first-mover advantage enough to become a major contributor to world carbon emissions. It'll eventually go away and be replaced with one of the alternatives that doesn't require the same energy burn.

> Privacy usually implies decentralized

Not really. What is decentralized about your parents knowing everything about you, and still being privacy-respecting?

Perhaps you meant anonymity implies decentralized, which is debatable too.