Considering that most rich first-world countries aren't having enough kids to keep up the rate of replacement, I don't think this is going to be reality. There's a strong correlation between quality of life going up and birthrates going down already, no need to sterilize people.

Also—we're already living in a world where a lot of menial labor is automated. I'm not sure I'd call it "utterly delusional" to see that there's a long history of humans automating tasks and to think that eventually we'll automate everything we need to survive. We've been moving towards that goal for the past 200 years!