The problem with taxes & subsidies is that their discriminatory power is not as great as policy makers would like to believe. They tend to either not work at all, or they work too well and overshoot the target. (This is the issue with many other economic interventions as well.)
Economists like to pretend that everything is a continuous function of price, but this very rarely reflects real markets. Most utility functions are step functions; there is some point at which changing your behavior becomes economical, and above it everybody switches, while below it nobody switches. People can either afford to raise a child in the lifestyle they expect, or they can't - and many of the sacrifices in lifestyle don't move the needle in fundamental living costs. For having a child, that point appears to be in the hundreds of thousands of dollars. If you make childcare and college free and give 2 years of maternity leave and ensure that you can buy a 3BR+ house on an average income, then sure middle-class people will start having kids again. All the middle class people will start having kids again, because they all face the same economic constraints. And then you'll have fertility > 2 again, and the population will start exponentially growing.
You could have a large per-child subsidy and cap at 2, but this also is a lot harder to generate the desired effect than expected. Accidental pregnancies are a thing. Twins are a thing. Infertility is a thing. Careers are a thing. People who want to remain childfree regardless of cost are a thing. If you cap at 2, you'll get a fertility rate under 2 because of all these other considerations.
And this is what's playing out empirically across many countries right now. A lot of European countries have generous subsidies for childbearing; they still find that they can't raise the fertility rate above 1.5 or so. China lifted its one-child only policy, moving it to 2 children in 2016 and 3 children in 2021, and finds that fertility still collapsed (even after instituting subsidies) and they can't convince people to have babies. There are significant non-monetary costs to parenthood; it's a whole other lifestyle, and the money involved needs to be pretty large to alter that.
Economists like to pretend that everything is a continuous function of price, but this very rarely reflects real markets. Most utility functions are step functions; there is some point at which changing your behavior becomes economical, and above it everybody switches, while below it nobody switches. People can either afford to raise a child in the lifestyle they expect, or they can't - and many of the sacrifices in lifestyle don't move the needle in fundamental living costs. For having a child, that point appears to be in the hundreds of thousands of dollars. If you make childcare and college free and give 2 years of maternity leave and ensure that you can buy a 3BR+ house on an average income, then sure middle-class people will start having kids again. All the middle class people will start having kids again, because they all face the same economic constraints. And then you'll have fertility > 2 again, and the population will start exponentially growing.
You could have a large per-child subsidy and cap at 2, but this also is a lot harder to generate the desired effect than expected. Accidental pregnancies are a thing. Twins are a thing. Infertility is a thing. Careers are a thing. People who want to remain childfree regardless of cost are a thing. If you cap at 2, you'll get a fertility rate under 2 because of all these other considerations.
And this is what's playing out empirically across many countries right now. A lot of European countries have generous subsidies for childbearing; they still find that they can't raise the fertility rate above 1.5 or so. China lifted its one-child only policy, moving it to 2 children in 2016 and 3 children in 2021, and finds that fertility still collapsed (even after instituting subsidies) and they can't convince people to have babies. There are significant non-monetary costs to parenthood; it's a whole other lifestyle, and the money involved needs to be pretty large to alter that.