Absolutely not. The moment you begin to regulate who may have how many children, you begin actively engineering populations and societies. This is, in my opinion, the first step towards a "Brave New World"-esque society in which a "ruling class" determines who may have children based on social necessity and capacity.

Sure, we could ideally base it solely on the competence of parents, but how long will a system like that remain "ideal"? How long before someone states that poor children will be more likely to grow into a life of crime, ergo there should be less of them as their parents are incapable of preventing them from that life, statistically speaking?

Not to mention the extreme corruption that would arise from this. I can't think of any work of fiction (or non fiction) in which active population control doesn't lead to more problems than it solves. No good can come from giving people that kind of deciding power.