Interesting topic. You make some good points. I find a couple that I do not necessarily agree. For example, "the world is overpopulated". I'm not so sure. Flying over most of the USA or Canada there is a lot of empty space. It is not built up today, but certainly if places become too crowded people can migrate to lots of virgin territory. The overpopulation myth seems to focus solely on cities.
I do agree on the very important point of education (and by extension, standard of living) and birth rates. The higher the standard of living, the less children people have. Typically children were had due to the boost in labor. Nowadays it is for different reasons (in the West).
I would argue against using force to limit the number of children people have as this is immoral. Any initiation of force is immoral. However, your second point hints at a solution. By removing the welfare state, there is no benefit to people having children for the sake of an income. If, on the other hand, we work towards improving education and raise standards of living, then the birth rate will naturally decrease.
One thing to note, though, is that if birth rates fall too dramatically, this signals a death spiral for a given society. That is, less newborns to replace an ageing population. Japan is an example of this. So we really should be careful what we wish for. Thanks for sharing.
RE: Should everybody be allowed to have as much children as they want