In 2008 I did a study to determine the effectiveness of government imposed birth control. Unfortunately, after searching for the paper I was unable to find it. However I remember gleaning these three interesting conclusions all based on effective implementation of the policies:
If people were only allowed to have one kid max per family per or better yet per couple the population would dwindle at an incredible rate.
If they were allowed two kids the population would grow 3 times before evening out. taking into account elderly and infant people alive today increasing lifespans and people having children later with medical advances that are being made provinf all things progressed at the same rates they were in 2008 which sadly I think we have managed to make these rates increase rather than decrease which mean totally different things for today.
If however, a share system was implemented where women were given 2 certificates kept in medical records which allowed them to have one child each the only exception being multiple births after already having had a child, and men were given certificates for up to 1 kid with exception to a mutiple birth. In this scenario after your record showed you to have reached the limit you could be/would be "temporaily fixed" making it possible for 2 men to have 2 kids with one woman thus allowing for 3 people to have 2 kids or 1.3 kids per person. With such a system we could get the population to even out relatively quickly and keep population numbers relatively stable. If Something went wrong and populations faced a threatening drop people could be unfixed to be able to have kids again and new certificates could be issued. A system like this would actually make sense seeing as how often twins or even higher numbered multiple births occur which would automatically bring a woman to her limit and likely also not put us over the edge in terms of population growth as there would be those born infertile and those who simple would not reproduce for other reasons. It also makes room for a reversal if things go badly.

Of course, these ideas only really work out as planned in controlled environments, in practice it did not take into account secretive births, and immigration which would not apply in world system. So far China is the best example we have of a 1 kid rule but there were exemptions made for minorities and some provinces had relaxed restrictions making it not really truly well enforced, also life expediencies have grown, the result being, the population has more than tripled since the Chinese 1 kid rule went into effect in in 1961. Japan on the other hand with its 2 kid policy saw it population numbers decline though they originally though tit would maintain the population and they are going through a population crisis where they are depopulating and trying to encourage more births now.

Obviously a series of rules and changes implemented as needed to them could be used to control the population and get it to a sensible level for example making it so at first couples would only be allowed to have one kid until population got low enough so we could handle 3 times the population evened out and then kid per couple numbers could be increased. But when problems are this big, there are never cut, dry and easy solutions.

My winded comment above was more to show that there has been large amounts of thought applied to the issue and thus far no real solution that works in practice. this problem also applies to the solution of edcating women and giving them access to birth control. Bill gates point also point out that controlling the population is not the best solution if one goes to the link I provided and reads further as it labels population as only one variable in the solution and states that in the best case scenario tackling the problem from a poplulation stand point will not solve the problem threatening the world right now. We need to Innovate to Zero as the so called elite are pointing out but population control will not solve the issue. Bill gates is trying to draw attention to the amount of CO2 put out per each unit of energy and pointing out how we must instead focus on this rather than the other three factors being population, the services we use, and efficiency of energy use.Any of which if brought to zero would solve teh world crises but for obvious reasons reducing these last three mentioned variables to zero is not a realistic approach.

I too would prefer keeping the government off and out of my balls and your uterus, LOL ;)