By the time the person without children retires, they already completed the duty of supporting the previous generation, making your case for a tax weaker.
You're conspicuously failing to account for the burden on society, the economy, and the environment that your children and their descendants will inflict, which is exponentially larger than a single non-breeder's finite contribution.
And you're also not addressing the fact that maximizing the number of humans on the earth is too much of a good thing, and makes life much worse for an exponentially larger number of people in the long run. Fewer people will suffer the sooner we slow and even gradually reverse population growth.
And you're incorrectly assuming that the only alternative to exponential population growth is sudden extinction, when it's much more likely that sudden extinction is actually the most likely result of overpopulation, due to ecological and climactic collapse and war.
If parents really altruistically cared for the wellbeing of their children and their descendants in the long term, and they're not just self-servingly and short-sightedly breeding in order to make their old age and retirement easier, then they should have fewer children to reduce the destruction they inflict of the environment from overpopulation, and stop driving their children to and from school in gas guzzling SUV minivans, when they could just as well ride their bikes or take a bus or public transit.