In general, maintaining a data structure isn't 'wasting power' albeit this is indeed taken to extremes with blockchains.

The idea of running non-cryptographic PoW has been around for a while. There are a lot of technical issues to deal with and a few mindset shifts as well. I am positive GridCoin sorta deals with it in the viable way.
Main problem is GridCoin isn't running the computation itself but running on another system (BOINC). In the real world, we could discuss this is mostly the same thing... but no, that's not the 'non cryptographic PoW' at work. Does that make any difference? I cannot tell.