It is important to understand that it is critical for the work to be "useless" in order for the security model to be the same. If the work was useful it provides an avenue for actors to have nothing at stake when submitting a proof of work, since the marginal cost of block construction will be lessened by the fact that the work was useful in a different context and therefore would have been done anyway. This actually degrades the security of the network in the process.
As a separate issue, proposing a hard fork in the hashing algorithm will invalidate the enormous amount of capital expenditure by mining entities and disincentivize future capital expenditure into mining hardware that may compute these more "useful" proofs of work. This is because any change in the POW algorithm will be considered unstable and subject to change in the future. This puts the entire network at even more risk meaning that no entity is tying their own interests to that of the bitcoin network at large. It also puts the developers in a position where they can be bribed by entities with a vested interest in deciding what the new "useful" proof of work should be.
All of these things make the Bitcoin network worse off.
Keagan