From what I understood, you wouldn't need to prove P=NP, you would just need enough computing power, as in, on the order of a few RTX 3090s.

Computational complexity was one of 6 reasons the author listed at why the optimization problem was infeasible. I read the article in its entirety, and I saw a claim that the number of calculations scaled in polynomial time, but I didn't see any claims of problems that are verifiable in polynomial time with no known polynomial time solutions.

Then there's the other 5 criteria, which show that this is not a computer science problem. Coming up with an objective function is entirely a subjective matter. It depends entirely on what the ruling party wants. Communist countries don't act to the benefit of all, they act to the benefit of the chosen few, just those few are chosen differently.

No, as long as humans are involved.

Capitalism/Communism are economic systems not political. It's all about how you distribute limited resources (Simplistically - All to a few vs a bit to everyone).