I see it that way too. That is the generational contract we have with each other.
Yet presently, with around 1.3 children per woman (where I live), this contract will not be fulfilled. All modern societies are moving below self-sustainability in terms of birth rates. This decline was already foreseeable when the contraceptive pill was introduced; and even before that, birth rates were falling in affluent societies.

Families are though the cornerstone of societies. Once families are in minority, and you have singles or non parents in a majority, society in general starts to degenerate.

Yes, parents are well advised to save money for their old age, but even that is not safe. Your funds could become vulnerable and even victim to economical crisis, as history gives evidence of. When a financial crisis hits hard, all funds may go to ashes.

Governments could, if they wanted, set on programs which promote and support family building long term, beyond any legislation period but with time scales around fifty and hundred years. Like they did in Hungary, for example (of which I am not saying those are long term, since every election can turn things around). Our government did not push it, though it also did not abandon benefits for families.

We promote divorce, enmity between male and female, between parents and children, not because it is intended on purpose, but because of the shift of focus and traditional values being too less respected in general. And the new age and "self actualization" became a thing. A lot of it is utter bollocks.

It may turn, though. I think the atmosphere shifts and the value of traditional family planing, marriage and other Christian related issues may have a comeback. I like to be optimistic for future generations, even though we ourselves as babyboomers will face the backfire of what we have missed to do on our own (myself included).