It's not even always the optimal strategy playing prisoner's dilemma. If all your opponents are playing "always defect", playing Tit-for-tat will consistently lose (because of the initial good-faith attempt at cooperation).

Right - if I recall, the story is that there were computer-simulated tournaments in which different strategies for playing the iterated prisoner's dilemma were pitted against each other, and tit-for-tat is the strategy that emerged to be the winner. So it's an empirical result showing that it is generally the most successful strategy, not mathematically shown to be optimal against every strategy.

It's not about the specific game nor the specific payout. When raising children, it's more important to teach/demonstrate that negative behaviour does have negative consequences.

I was responding to a claim about what game theory tells us.