This is insane. I have heard this question for years, implying that somebody else should decide if you're qualified to do something that is none of their business.
Who would enforce this entire thing? Let's see... Probably the men and women who do business at gunpoint, who call themselves "government". Are we really going to ask for them to have more control over our lives? Are we aiming for a Nazi-like world, where the men and women who call themselves "government" decide who lives and dies?
I believe this is one of the "holy grails" of the tyrants... To get public support for deciding who is allowed to reproduce.