Magistra Ygraine, I am a long time fan of this idea, and have had versions of it myself.
I've often referred to it as "parental licensing". My criteria is slightly different from yours, but on the same thread:
1. Proof financial security. There could be a set amount that a household would need to earn, along with a credit check (to see how much debt is with that household) in order to prove that they can afford the child.
2. No felonies within a seven year period. Truly, I'd say no felonies ever, but I don't think society would go for it, especially when there are enough examples of felons cleaning up later in life and living responsibly.
3. High School diploma or GED equivalent. While I know that there are many examples of high school drop outs going on to start their own businesses and make some considerable loot, this criteria is in there also as an incentive to keep kids in school, and serious about passing their classes. As a high school educator, I'm partial to this one.
I like your added prior agreement to custody and support issues. That too makes worlds of sense.
What I'm unsure of would be the method of sterilization. I don't think that society would go for reproductive surgery on newborn infants (even if they are willing to circumcize many of them).
I've tossed around the idea of a form of birth control in standard drinking water, but the cost might be large, and the chemical logistics of one batch of chemicals doing the whole job without side effects is a tough challenge to work through.
Either way, you are correct in the large benefits it would have. Zero unwanted births would mean a large chunk of social welfare would be lifted. Abortion issues become non-issues. We'd have a society where nearly all children are cared for by homes that wanted them in the first place. Our education level would rise in America by large amounts.
Fucking Utopia indeed!
"Extraordinary claims require extraordinary evidence."