In the deleted OMR scene, River hasn't just considered breeding, she's pushing for a shotgun wedding! I've read a gazillion stories where Kaylee and Simon have a baby, and a few where Kaylee and Jayne do and I daresay she has thought about having one or more babies when she's through having Adventures. She reminds me a little of Ann Whitefield in "Man and Superman"--looking for "A father! A father for the Superman!"

Oh, yes. I should've been more precise in what I said. I meant that Zoe's the only one we see in canon who's got someone actively pursuing her for the purpose of procreation.

I suspect that one of things going on in HoG is that Companions are temporarily or permanently sterilized,

That makes a lot of sense to me.