Sorry, that’s not enough. If you accept that individual human beings have strategic agency, they will try to get individual benefits, as well as group ones. Sometimes the two are in contrast. This is the essence of the free rider problem.
Are you familiar with dual inheritance theory? It stems from human evolutionary biology, in particular cultural evolution. The idea is that humans are eusocial animals, like ants, but not quite all the way like ants are. They cannot be, because of fundamental differences in the reproduction cycle of mammals vs. insects. So, whereas most animals (say, hawks) are subject to natural selection at the individual level, and eusocial insects are subject to natural selection at the group level (with the twist that each member of the same ant colony has exactly the same genome), humans are subject to natural selection at both levels.
Group-level selection rewards good collaborators, altruists: success of groups depends overwhelmingly on their ability to collaborate. Individual-level selection rewards selfish behavior, sociopathy, free riding. As E.O. Wilson puts it:
the human condition is an endemic turmoil rooted in the evolution processes that created us. The worst in our nature coexists with the best, and so it will ever be.
So, imagine you are a club bouncer in Numbercaste. You are supposed to only admit people with a Number above, say, 1,000. That is how the club would perform best (supposedly). But if you were to accept a discrete bribe from a low-number individual to let them in, you personally would fare best, as long as you are not found out. The tension continues on. There will be a pressure to hack, delegitimize and disable these systems. I mean, look at democracy! It is in a nations’s interest to have a functioning one, with dignigity and high trust in institutions, but plutes subvert it, because that’s good for them.
So, no, “it just work” is not a Nash equilibrium under DIT. 