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.