No, mining computes useless SHA256s. It's only purpose it to decentralize block production which can be done with POS or other consensus mechanisms.
The belief that mining somehow "backs" or adds value to bitcoin is like a cult mentality. "The bitcoin algorithm does jobs currently held by ..." - except these parts can all work fine, you just skip the part where you do a billion hashes.
The entire Bitcoin network uses less energy than one out of thousands of large banks like the Philippine National Bank.
Satoshi believed, as do I, that miners by competing with each other invest in equipment and power equal to the value of the mining reward. He said . . .
It's the same situation as gold and gold mining. The marginal cost of gold mining tends to stay near the price of gold. Gold mining is a waste, but that waste is far less than the utility of having gold available as a medium of exchange.
I think the case will be the same for Bitcoin. The utility of the exchanges made possible by Bitcoin will far exceed the cost of electricity used. Therefore, not having Bitcoin would be the net waste.
The cost of proof-of-work is not merely equal to the power used, it is indeed equal to the mining rewards - $557,358,000 annually at today's quoted price.
I concede that this is a lower figure than the 10% of the world's economy consumed by the financial sector, yet it is a waste because Satoshi could not conceive of proof-of-stake, nor did he debate the concept. The existing idea of hashing proof-of-work instead was adopted for Bitcoin.