Thought experiment for all the unrestrained free-market folk: how can the free hand of the market can solve for low birthrates? Bonus points if the solution doesn't involve government-issued visas.
This inner desire wasn't selected for strongly in the past because there were other mechanisms to nudge people to procreate (social norms, lack of birth control), but I expect it will play a much bigger role in the following generations.
What does free market have to with it?
tax cuts for families, subisidies for child birth and care - none of these are contrary to the idea of a free competitive market
Moreover, a free market can benefit from regulation and certain socialist policies (eg. transportation and education).