We don't have to reduce carbon emissions by 20% in 50 years, we have to reduce them by >100% in less than thirty years. Reducing birth rates is both, much too slow, and not sufficient (unless you propose reducing population to 0).
Is there any solution could really reduce around 20%? (Not to mention more than 20% and not to transfer the emission to other countries)
Each of those saves on the order of 20% of emissions and could be done in less than a decade if we put maximum effort into it.
I really doubt convincing a sufficient number of people to not have children is easier than any one of those measures. Just imagine the political backslash if the government suggested not to have kids for the climate. It's a lot easier to convince people to stop eating meat for the climate and even that is essentially impossible.
In the scale of country, East Asia did quite well without any policies (exclude China, they have a special policy on it). Just keep raising the price of estate, and then birth rate would drop and never come back.
For the part of energy, according to the EPA report[1], the emissions by electricity and heat are around 25% in total. If we want to reduce 20% in total, we need to close 80% of fossil plants. For me, it is nearly impossible. There are some countries may not have the land or safe area to place nuclear/renewable plants. (e.g. Singapore...) I know there is a plan for Singapore to buy the clean solar energy from Australia, but it only covers 1/5 of the consumption. Also, there must be security issues for transferring power between countries.
[1] https://www.epa.gov/ghgemissions/global-greenhouse-gas-emiss...
https://www.sunseap.com/SG/newsroom/2021/sunseap-signs-MOU-w...
I suspect most westerners are not going to be thrilled when receiving the government email about their mandatory sterilization.
Usually the idea floats in circles of people convinced we'll reduce the birth rate of "other" people (wink wink dog whistle yeah they're thinking of Africans)