Proof of work is just some mechanism for a 3rd party to verify you actually invested “value” into the chain. That’s a PR.

Are there any traditional block chains where the proof of work is actually an investment into the chain? Such that the structure of the chain represents something of actual value (not a series of rare hashes), and additions to the chain add to that value? A la git. One potential example would be neural networks on a chain, where the work is training the network, and the value is intrinsic in the well-fitted resultant model.