I wonder if a better one sentence conclusion might be something like "Predictably nice players consistently distribute their gains to the group". After all, the interesting variable here is repeatability; that is, as certain players learn which players are consistently "nice" through repeated trials, they get iteratively better at gaming them to forfeit their (potential) gains.

In other words, over time, the "compound interest" on the gains the nice individuals lose gets rewarded to the group. Any individual in the group who can game "niceness" benefits the group at the expense of the nice individual. "Good guys finish last," or something of that nature?

Stabilized long-running cooperation seems like a very bad desired(?) outcome, by the way; is that what you're saying is a good thing? Pareto improvements are usually realized / discovered / gained by individuals who eschew tradition and playing nice.