We had a sort of discussion here the other day on the reverse of this - giving credits for NOT having children (some environmentalists believe this measure could help save the environment) - and I have to say - my position for that is the same as for the one you stated here ( … it’s legitimate for the government to take an interest in a woman’s reproductive decisions and incentivise some behaviors… ) -
I think it’s an awful idea. Either way.

IMHO environmentally-motivated discincentives are pointless, because any reduction in population will be compensated for by an influx of immigrants to make up the numbers. Economic realities more or less dictate that. Incidentally that’s why a lot of these nativists/rightists take such an interest in reproductive issues, they figure that if the birth rate goes down then more immigrants will be brought in to balance out a demographically top-heavy “aging” population.