The hidden hand of self-interest already produces the optimal outcome. Risking up to half the population's lives for nothing but the warm fuzzies of having participated in a "cooperative equilibrium" is insane. In the red-blue puzzle, there is no aggressor to be fought. The problem is purely circular and nothing of value comes out of it.
This nearly perfectly captures the different frames people use to analyze this problem and the argument in favor of fostering blue-button-pressing.
Red-pressers tend to frame the button game as a single isolated decision problem. For blue pressers, what's at stake isn't the button vote but what the disposition to press blue indicates about everything else someone does. These frames talk past each other.
The disposition behind those “warm fuzzy feelings” about cooperation, which red-pressers consider naive or insane, is precisely what extends cooperation beyond the reach of pure self-interest. The warm fuzzies are the emotional reward humans attach to loyalty, honor, fairness, and cooperation. It is part of the machinery that makes costly cooperation psychologically possible.
To be fair, I can work with honest red-voters. Predictable self-interest is much better than fake virtue. The people to be wary of are those who virtue-signal blue and then vote red.
But I would still rather have honest blue friends than red friends.
Reds will save themselves. I can work with this if they're honest with me. But blue friends will side with me even against an enemy that might win and kill them. Blues will fight wars and enforce norms against defectors to achieve outcomes they might not personally live to see.
Someone has to be willing to pay the founding costs of trust, law, and cooperation. To do this, you must identify with a cause that transcends self-preservation. You need a willingness to die for your principles. The warm fuzzies are the human machinery correlated with blue-pressing. This is the machinery that motivates people to bear founding costs that pure self-interest would tell them to externalize.
Red preserves the self inside a low-trust world. Blue is one of the dispositions that makes a high-trust world possible.