Norway is close to providing all of what you describe and still seeing well below replacement fertility rates. It maybe be a start, and it produces a far more pleasant society, but it's not enough.
There are other concerns as well related to cost of living.
Even though we would like people to live outside the cities, cities attract a lot of potential parents. They end up in a situation where they have a long education and start their careers late and don't have the financial capability to get a decent family friendly apartment in the city. Many wait until it's almost too late, and having more than 1 or 2 is definitely not something most wants
The average age of first-time mothers is over 30 years old. A single child may be something the family can handle, but more than 1 or 2 forces the families to move outside the cities to be able to afford a house in addition to hurting the mother's career.
Tldr:
- Cost of living in the cities are too high
- If a second (or third) child forces them to move out of the city, many increasingly choose the cities
- Having more than one child after 30 will have a negative impact on the career as they simply can't work as many hours and has to spend long periods away from work
I think you can simplify that: Standards rise as living standards rise. People want more both for themselves and their children when they see that as realistic, and opting for fewer children is a way to make that happen.
Yes, I think that covers everything in a concise way.
If we want to go back to a sustainable birth rate, we need a wide range of actions. Some may require to reduce the financial risks, while others require encouraging cultural changes.
