What is the concept behind 人不坏，没后代?
I asked a few of my students about this, and they mentioned something about sex being bad, too.

In a nutshell, there's nothing that doesn't have some bad aspect to it, even the best things.

One student specifically mentioned the second variation, 男人不坏，女人不爱，没有后代: "if there weren't bad boys in the world, women wouldn't fall in love, and that would be the end of it, wouldn't it?".

As for the variations about the animals, maybe it's just for the rhyme. But the one about bad men/boys, you seem to have the right idea.