Yes, they start out with game theory, which is only about rewards, and then add in punishment.

Game theory is enormously insightful, but It leaves out a great many factors that are very important in the real world, such as communication between the parties,uncertain rules, and reputation.

All the factors you mention are accounted for by researchers that use game theory as the basis for evolutionary modeling (for a primer, check out "Evolutionary games on graphs" - https://arxiv.org/abs/cond-mat/0607344).

Ok, I was confusing the prisoner's dilemma with game theory as such.

what about other cooperation methods beside punishment. why are they less crucial?

Society already includes many forms of punishment, and there is no way that would ever change. The question is which forms of punishment are helpful and which not, and the social scientists can answer that question only if they include it in their studies.