Proof of Processing (resource)?

Continuing the discussion from On creating SAFE alt-coins:

I’m sure this has been discussed by a lot smarter folks than me, so please excuse my naivety and ignorance. Please point me to resources if you know of any, so I can educate myself better and not be so ignorant on the subject from here on.

Mining crypto (POW) uses a lot of processing power. Why can’t we harness that computing power in a type of proof of resource or work? Say people create calculation files that are used to complete tasks. Why couldn’t clients download from a pool of encrypted files (they don’t have to know what they are processing) and process encrypted data on their machines as a type of mining work? Rather than setting a difficulty for solving a hash, why not require a certain amount of processing?

OK - I didn’t search enough. This has been talked about quite a lot it seems.