That would not work well. Most western countries already have very low birth rate and will get into a lot of problems because of it. It is more sensible with a gradual population decline in each country.

Instead of pushing families to be childless we should help those who typically get 6-9 kids get fewer. You make everybody more happy that way. It is not great for families to struggle with raising six children. Nor is it fun for a lot to be childless.

A sensible goal is to have a max of two children. That will give a gradual decline we can handle.