my response is admittedly whataboutism, but it's worth comparing to say, the dollar. The cheeky answer to "what backs the dollar?" is "guns, missiles, and aircraft carriers" but in reality it's "growth". The cost of the extant financial system isn't, say, the sum of bank branch construction & bank employees' gas commuting to work, etc -- it's the sum of all economic activity driving growth, which as of now is still inextricable from dirty resource extraction, conversion, and movement.

Which isn't to say it's OK to throw bitcoin mining on top of that, or that bitcoin can fix it. Just that we're on an unsustainable trajectory with or without it, barring an energy revolution or a very painful collapse -- at which point I suppose we can just plug the miners into the local fusion plant (or trade in ammunition and the chit of the local warlord).