I've been thinking for a while that proof of work should be replaced with some other type of real work, such as training a Neural Net, but that runs into major issues after thinking about if for more than a second. Hopefully though, someone much smarter than me can figure something out

The "value" must be produced outside of the crypto system then moved into the system as a value store. I don't know how this is not an obvious concept.

Thats one of the very obvious drawbacks.. Money is a store of value, but crypto just tries to 'be' the value, which doesn't go well, because well it's not valuable at all

It produces objective immutability of the transaction history.

It's a terrible way of doing that, and it isn't even necessary to produce an immutable record of transactions. Seriously, spend some time thinking about other models for distributed transaction records.

Blockchains are designed the way they are to prevent governance and oversight, meaning, if someone scams you or steals from you, there's no way to get your money back. "No backsies" is the most fundamental principle of their design.

Isn't it subjective immutability?

Your transaction might disappear from the history if the view changes to have some other branch be the accepted one

The PoW on top of a tx produces immutability in the sense of a minimum cost imposed on a rewriting of that tx. If no attacker is willing to bear that cost, then the objective longest chain rule (i.e. most cumulative difficulty) will preserve the history up to that tx. Without PoW you have no objective way to determine the true history.