Ah, ok, well let me lay out my argument for why it has utility.
Your bank and other organizations (Western Union, etc) spend a great deal of their time and money to create and maintain networks that permit them to move money from one place to another on Earth. Your bank probably pays to some network in order to be able to send and receive "wires" of money to and fro. Migrant workers use Western Union and the like to send money from the country they work to their families back home. For this, Western Union and the global banking networks charge fees. The fees charged by bitcoin to relay funds can be significantly lower. Probably not universally so, but I'd say all transactions above a certain dollar amount would be cheaper. They'll probably be as fast or faster than traditional remittances. Bitcoin does this as good or better. Western Union and friends could decide that leveraging the bitcoin network might actually be cheaper than their current network, or they might be forced to realize this by competitive pressure from other bitcoin-based remittance companies.
Ok, so that is one use that is IMO unassailable. The people on this planet is putting money into building retail locations for Western Union, they're paying for the power to keep the lights on at Western Union, and they're paying the salaries of the employees at those retail locations, and the folks who staff the armored cars moving the actual cash from place to place. That's not a waste, right? It's spent by us collectively in order to get that value. And maybe bitcoin's difficulty-scaled PoW is not spending electricity well. But it's useful and that's why people do it.
Now your claim is regarding the value of entropy and I will claim that you cannot get a mechanism with bitcoin's qualities (trustless + equitable distribution) unless you have a PoW. But I will concede that you can have a delegated-trust proof-of-stake coin that has some of bitcoin's qualities without a proof-of-work.