Evolution, either genetic or cultural, doesn't have infinite search capacity. We can evaluate which of our adaptations actually are promoting or enforcing symmetric cooperation in the IPD, and which are still climbing that hill, or are harmless extraneous adaptations generated by the search but not yet optimised away by selection pressures.

But we are our adaptations. Are you claiming morality should be defined by evolutionary fitness? (So we should tile the universe by our DNA?) How is that better than other external sources of morality? We already have a morality, it doesn't matter (for the purpose of being moral) where it came from, be it God or evolution.

Also, saying the morality comes from solving PD doesn't help, since PD already assumes the agents have utility functions. Game theory is only directly relevant to rationality, not morality. If you and I are playing a non-zero sum game then we better cooperate for our own good. But the fact that my utility function already includes your well-being is completely independent.

I agree that evolutionary thinking can be helpful to figure out what our morality is (since moral intuition is low bandwidth and noisy), but I'm against imaginary extrapolations of evolution.