Do you think having children is a fundamental human right? Should there should be any restrictions?
1) Probably, yes. 2) Probably, no.
Yes there is a population problem, if one wants to define it that way. There is also a greed problem. It seems easier to prevent people than to prevent greed, but that doesn't make it right. Population control by policy sounds like a good idea, but we have always screwed it up and will continue to screw it up in the future. Birth control by public policy doesn't even sound like a good idea and we are even more likely to apply it unjustly. We can let nature take its course, especially when we find out what nature is and what nature wants. That's the problem we need to work on.
There are two kinds of restrictions -- quantitative and qualitative. I believe i have addressed the quantitative issue above. It seems reasonable but we are bound to screw it up. Qualitative restrictions are even worse--remember the eugenics movement, remember Hitler. There are some kinds of people the world just doesn't need, i'll bet i can name two, but if i try to name a third, i will probably contradict your list. Even if we admit that certain people (human vegetables? serial killers? world conquerors?) should never have been born, there is probably no reasonably accurate way to predict which of our children will end up in one of those categories.
So we are stuck with our blind, and so far misdirected, groping toward a better world. No population policy, please.