You've missed the main reason: children were always a pension mechanism, and today we have socialized (, and private) pensions. There's no need to have children if you think, in the end, the state (, or you bank account) will look after you.
* take it from a young parent that also knows a lot of other young parents - that's really not the reason. We are older millennials, and none of us expects to have a liveable pension anyway, we all save separately for old age if we can.
* it's not the "state" that is supposed to look out for you, but your own money invested during the career. I see that money subtracted from my paycheck every month. I only want the state to provide stability and security so that money can be put to good use.
Birthrates are declining in places (like the US) that do not have socialized pensions. (Social Security is not that... secure. And regardless, it's existed much longer than the recent birthrate decline here.)
I think you're missing that people generally and innately want children, irrespective of "pension". If people aren't having children, it is because of sufficient negative incentives, not because of "pension".
