Yeah OP, you are right.
In the "old days" and still in many countries, children take care of their parents in old age. It's necessary, and expected, and there is a lot of moral value placed on that.
People who find themselves without kids in those societies are at risk, and often need to rely on nieces and nephews or even cousins. Or they have no one and really suffer.
We have created a society where elder care is commercialised and financially speaking, socialized, and the people doing the hands on elements are not usually your own children, they are other people's children. Chances are that even if you have no children other people's children will keep society running, pay taxes, and manage your care.
So compared to other societies, there is little risk to being without kids. And in fact you may be better off, because you will have saved a lot of money by not having children.
You will, however, still be dependent on other people's kids to wipe your bum and grow your food and deliver your groceries.
We have socialized some elements of child-rearing, particularly education. But I would argue that it's not really balanced out now. It's still a massive expense for parents, without the security that historically would come from having children. And it's a significant impact on why people don't, and often can't, have children.
Long term it will be a problem and in fact we see that already.