I think I understand the GP pretty well. Cheating, or defection in the language of evolutionary theory, is subject to frequency based selection, meaning it is strongly selected against if its frequency is too high in the population. It's not a stable strategy.
It can be a winning strategy for a few individuals in a cooperative environment, yes, but it breaks down at a point because the system collapses if too many do it.
And yet, cooperative systems are common and stable, which is my point.