> Are you suggesting that only people who have kids should be given assistance when they grow old and frail?
It was the case a century ago. Society wasn't much worse off. But even with pure private retirement planning, it doesn't fix the issue that there are less and less productive members of the society as the population ages, while the needs increase.
> Whether to have children or not should be a personal decision
Which ends up affecting the whole society in aggregate. If my car pollutes too much, it's ok, but if too many people has the same car, then it becomes a problem. So society decided to add incentives to reduce the car pollution (in this case, fines).
> Funny thing is if people suggested forcing people (directly or, in this case, indirectly) into not having children, people would be up in arms about it.
The Chinese experiment shows otherwise.
> How is it alright, meanwhile, to be forced, directly or, again, indirectly in this case, to have children?
You can add fiscal incentives, many countries have them, condition old age benefits to how many children you had, or public care homes' access, etc. This also allows to free ressources to help today's childless people and parents to have more children.
Ressources are not infinite and at some point we need to choose if we prioritize old people or young people. My point of view is that this prioritization should depend on how many children you had. If you invested time, money and energy (I had to wake up 4 times to feed my daughter last night, for instance) to perpetuate society, why would it treat you the same as the people who didn't want to do the same effort?
Not having children is a personal choice, but it doesn't mean that it should be free of personal consequences.