You aren't wrong but to me you are focusing on the wrong things. As you say, the west is already dropping the birth rate and being more and more focused on sustainability, etc. Eventually, it will get there. Change takes time.

The big problem is the 3rd world. People there don't a have a choice. They don't want their family to starve. Women are largely forced into a reproduction role only. But we know that the way to reduce birth rate is to educate women and give them jobs and careers. We know that if we can create stable jobs in the 3rd world, they will stop clear cutting forests. To me, that is where the billionaires should be putting their money. If we raise the global standard of living enough, our high population problems will slowly revert.