The primary purpose of the precepts isn’t to provide a social good, as far as I understand. It is to provide a foundation for practicing the Dhamma. That the precepts also provide a social good isn’t accidental though. It is tied into the way that kamma operates; one can’t be intent on one’s own welfare and simultaneously have ill will towards others.
Game theory
Game theory posits two kinds of games. Finite games and infinite games. Finite games are played once while infinite games are played again and again. Depending on the game played, the incentives change.
The tradeoffs between living and practicing/teaching vs committing suicide change based on whether you are playing a finite game (i.e. only have one life) or an infinite game (i.e. have many lives). In a finite game, a person may well kill themselves to save other creatures, weighing their many lives over his one.
However, in an infinite game this equation changes. In in an infinite game, you would kill and be killed an infinite number of times so the best way to show compassion is to practice and gain awakening. The next best thing is to teach others so that they too can gain awakening.
This means that in the event that the primary purpose of the precepts is to provide a social good you would still be better off living and practicing / teaching because Arahantship is the results in the ultimate social good.
As an aside - if you are familiar with the prisoner’s dilemma, the outcome changes based on if the game is finite or infinite. In the finite game, two prisoners are incentivised to dob each other in and both end up going to prison. In an infinite game, both prisoners know that if they betray the other one that they will in turn be betrayed the next time. This incentivises both prisoners to keep their mouths shut and therefore go free.
This brings up an interesting point. Belief in rebirth is crucial to practicing the Buddha’s teaching to completion. Without rebirth (i.e. in a finite game), it doesn’t matter too much what one does. One suffers a little or a lot and dies, and that is the end of it. To the extent that one follows the teaching, great but because one dies, there is no big loss. One might even commit suicide to end the suffering early.
However, with rebirth (i.e. in an infinite game), it matters to a great degree what one does. The prospect of an endless series of lives lived in suffering provides the necessary incentive to follow the Buddha’s teaching to completion.
A beginner may get by without a belief in rebirth, but at a certain point the effort required will not be forthcoming until rebirth is considered as a serious possibility.