In terms of controlling population numbers, this kind of policy is not necessary. Humanity is already well on its way to a tragedy of the commons, and nature will balance it out, either with famine, plague, natural disaster, or all of the above. In terms of social responsibility and who "should" have kids, I see no way of uniformly putting into policy something so subjective.
You can't base it on money because rich people can be lowsy parents. You can't base it on age because the human lifespan has almost tripled in the past 500 years and the fertility boundary is constantly being pushed further.
I guess my basic concern is, who decides?
I'm in favour of eliminating programs such as baby bonuses which provide incentives for people to have kids for financial reasons. I am also sadly, but admittedly, in favour of mandatory birth control for people on long-term welfare, although in practice I think its implementation would be highly controversial.
Fertility programs are something I take issue with because of the numbers of children often produced, and financial screening should be mandatory for people who undertake these procedures. It shouldn't be as simple as whether or not you have the money for the procedure itself.
I guess in the end, I'm in favour of it in theory, but in practice I just don't see how it could happen.