You're still missing the point.

Not having kids yourself but still having a retirement of any kind is a privilege that only exists if most people still have kids, so that their kids become workers who will provide the goods and services you need to keep living in retirement.

Government pension doesn't magically continue to work if everyone chooses the individually optimal solution of not having kids and consequently having a much easier time saving more money for retirement. If everyone executed this strategy, all that extra money you saved would become worthless, because there would be no one to give you goods and services in exchange for it.