Not sure if you’re trying for eugenics, but it certainly sounds like you are.
Incentivizing sterilization probably means that marginalized groups will preferentially take advantage of it (well-off people can already take long vacations, etc.). So now we have a disproportionately sterile lower class, while the upper class can have kids as they see fit.
Don’t get me wrong, overpopulation is a real thing. But e.g. Japan’s declining birth rate doesn’t seem particularly happy, and I’m not sure government sponsored sterilization bribery is great either…