In pretty much all species that’s a factor. The healthiest looking females are most likely to be healthy, and thus bring the healthiest next generation possible into the world. The strongest and healthiest males try to claim those females for the same reason.
If you want a specific example of this, look at pack behavior in wolves. The alpha male takes the ‘best’ female for himself, and the other wolves have to make do.
And as for things like the baboon’s butt turning red, that’s not a sign of attractiveness in the individual, but rather a sign that she’s in heat and ready to mate.