That would work too.
If we incentivize those who are childless and have shrunk their carbon foot print, that would also encourage people to make thoughtful decisions about baby making. Example: If someone didn’t have any children at all, then they should get tax free status or reduced premiums etc.
A woman increases her carbon foot print 10-20 times with every child. Medical costs and food and transport and pretty much everything is borne by the rest of us. Suspend benefits. Tax excess children and give tax breaks or retirement benefits to those who didn’t have children.
I suspect that retirement benefits would be a better incentive than tax free status. Most people hope that children would take care of them when they get older. It’s not worth the true cost of over population.