What if you're wrong? What if, all else being as it is but with "lotsa child support programs and credits" and education, on average people who could give birth decide they're not keen and we do not hit replacement reproduction rates?

Because humans are so numerous even if we hit 1.0 rates (ie population halves each generation) we've got a long time before that's a pressing issue.

If the population halves each generation the biggest problem is total societal collapse. The children and the elder cannot be sustained by a small number of people of working age and the infrastructure cannot be maintained by a dramatically dropping population: even with AI and robots, roads don't fix themselves and train tracks don't get fixed by robots. We will not even have enough doctors and nurses to care for the seniors and no economy to make retirement possible (money will be worth their value in paper as there will be no people to provide services and goods for it).

If someone things the population on the planet is too big, then plan for a reduction that is manageable and change the pay-as-you-go pension system that exists in most of the world, that is based on working age people paying the pension for retirees. Even at replacement rate the pension systems will collapse, they were built in a time when the average number of children per woman was around 7 and the age of retirement was higher than average life expectation.