Hmmm... Perhaps that could be one component, but I don't know if proof of work in the typical way would be required? As in 'guessing' a hash (I don't know much about that area so I could be wrong here)., I don't think would be needed - but perhaps the proof of work could simply be 'calculate the output that you want to make anyway' - such as the weights of a neural network, a read only database to do complex queries on, an operating system compilation with specific configuration, a dataset of estimates of some physical science data using a particular algorithm, etc.

So instead of using CPU cycles to do finance/currency things (or whatever is done in that arena), this would calculate whatever data you actually want directly.

In some cases it could be a ton of calculation (estimating electron density functional, or training NN weights) to receive a small file (DFT functionals are quite small). Or it could be some calculation for a large amount of data (ETL for big we scraped data).

One important aspect which is similar to the currency/Blockchain realm is that the commits would specify the data state, so the data would likely be mostly read-only for people, but if they change it, it would simply branch off to a different hash pair.