However, "sustainable" implies that we're talking about the long term. Once the block reward no longer exists and mining is reliant on transaction fees, the money that is "wasted" would be based on what users are willing to pay for a Bitcoin transaction.
Considering that both miners and banks are working for profit, we could consider both the Bitcoin transaction fees and bank transaction fees in this scenario to be "wasted money". So then you're left with the question of which has higher fees.
If more people were using BTC and it had been scaled properly, it could theoretically have lower fees and therefore be less wasteful.
That said, BTC's current "waste" of electricity is important for its security. That's how the PoW system works.