I wonder if it's possible to create a blockchain where the proof-of-work consists of building a better compression-dictionary instead of doing useless hashing.
To give a little detail on why this is not possible, proof-of-whatever should be quickly verifiable while hard to generate. Compression might sound like it can achieve both requirements. However, raw data needs to be very large so that the problem is not trivial. Large data is a red flag in any blockchain application.