Nope. “Free” PoW undermines the whole system. Mining has to be a sacrifice, otherwise it won’t work anymore. There is no “and I can use the resulting infrastructure for X”. Every joule of energy that goes into proof of work is a joule wasted by design. There is no free lunch.

I’m starting to think that maybe cryptocurrency is the great filter. It’s actually pretty terrifying.

Edit: we should probably have termed it proof of valueless work to make that clear. There is also nothing to stop a speculative bubble crowding out all other energy uses. Our low-growth world is very vulnerable to these schemes.