I'm sure there is potential for abuse and corruption in such a system (as there always is), but I've often thought that the world would be a better place if breeding were more of a privilege than a right.
Four little words: The Maury Povich Show.
On a more serious note--where I presently work, there are a number of mothers who are under 25, and who have four or more children. Because they are young, inexperienced, uneducated, and sometimes traumatized, these mothers can't provide for their kids emotionally, intellectually, socially, and economically, and everyone (and I mean everyone
--the kids, their classmates, their kids' teachers, the society) suffers as a result.
Of course, such a system would have to be carefully structured and supervised, so that you don't end up with a situation where the person or the party in power exacts a straight-up genocide against some hated group.