I don't think that's the point. I think the point is that SD is closer to the average case for cooperation than the PD, so it might be a better tool, in general, for talking about and reasoning about cooperation. (Both PD and SD have the nice property that they are simple and straightforward, and both have the problem that they are only approximations.)
But even that's a tough sell for me, since the ideas you suggest as substitutes for the term "explain" are things I would put under the umbrella of what is meant by explaining.
Cooperation evolved in humans because:
a. Our young are helpless, and take over a decade to reach sexual maturity. Those who cooperate to raise the young have more descendants.
b. Cooperation is a sexual fitness signal because of point a
The end.
Edit: fix a word, thanks.
It's not clear to me what you mean by this.
In the example of the experiment in the example cooperate means the snow is cleared faster.
In my example cooperate means raise the young together.
> but most people don't choose to adopt
Because our biology drives us to want to have our own offspring. It seems obvious that if our biology drove us to want to raise other people's offspring we wouldn't be having this conversation. Although this has been an extraordinarily successful strategy for dogs and cats.
But just a few minutes ago you said our biology drives us to "cooperate to raise the young." Do you see how this topic might deserve some more study? Basically, my only issue with your comment is "The end."
However, if the idea is that a model is good at "explaining" cooperation by setting up a hypothetical where people choose it a lot, then I guess the "best" model would make people choose cooperate all the time.
So you can set up the points for cooperation to be infinity and the points for all non-cooperation to negative infinity. And you can wrap it all up in a hypothetical story about what the choices mean. Now you have a perfect model where people choose cooperate 100% of the time. But I don't feel like I'm any closer to understanding how cooperation evolved in humans.