Setting aside the advantages of Proof-of-Stake in terms of energy consumption, and setting aside the "green energy buyer of last resort" argument that the BTC maximalists often say, and setting aside the theoretical requirements for a valid PoW function, I do think it's tricky to argue which computing is inherently "valuable" or "not valuable".

There is this intuition that guessing a bunch of random numbers doesn't contribute high-leverage information or "work" to society. That there are a bunch of "information processing" tasks that have more inherent value.

But consider SETI@home - is decoding massive amounts of space noise valuable if nothing ever comes of it? Is the computation wasted?

Consider Folding@home - there are now far superior algorithms like AlfaFold that take far less compute. Is the computation wasted?

Consider all the matrices being multiplied on gigantic neural networks. Some of the resulting models will be enormously valuable to society. Most of it will be dead-on-arrival experiments - simply wasted compute. Even worse, the leverage can go the other way - a ML model can cause far more harm than the energy footprint used to train it.

One of the nice properties of the BTC PoW function is that you can be sure that your hash finding algorithm is probably not that sub-optimal.