Pay women a decent wage per child, like a good part of the average wage per child until the child turns 18. That’ll be a clear incentive to get children. Everything else is just ineffective tinkering. In a classic rural setting children were a labor force. In a modern urban setting they’re a very expensive hobby with lots of unpaid labor. In a quid pro quo world, pay up. Children are not free. If that’s not possible then a growing population is not economically viable in the current system. Better luck in the next system.
Some regimes have tried to force the issue, banning all abortions and contraceptives. The end result was a population that was shrinking more slowly and orphanages overflowing because children were dumped as people didn’t have enough money to support them.
What you say is correct and is also what is happening. Some have no children, some one of two. The end is fertility rate below replacement rate. Many people that want children stop at 2 because then it becomes too hard to combine with a job and costs too much. If there government wants more children, support is needed.