You seem to be misunderstanding the GP.
Evolution does not work maximizing individual success.
Evolution does not work maximizing individual success.
Yes it does. In fact, unless you want to get nit-picky about intra-gene, inter-allele selection, that is _exactly_ what it does.
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.
Chance to pass genes forward. This is only equivalent to individual fitness for very solitary species and humans aren't.
As an extreme example, take soldier termites - their chance to pass their genes is zero, but the chance for the colony to survive grows. Also gay people exist (they also - usually - don't reproduce, but help others instead).
Humans naturally care about their family and tribe because this increases the chance of their bloodline to survive.
In evolutionary theory this is made clear by using the term "inclusive fitness" - worker ants actually pass their genes on to future generations more effectively by taking the detour, if you will, through the queen.
If you want to be nitpicky and argue we should consider the individual gene the unit of selection, as Dawkins famously argued, I'm not going to disagree, you can see it that way too.
That specific distinction very rarely leads to different predictions though.