You're missing out on the effect that children will have in that system. Children will still be there, to keep the population stable, and because some people do like to have children, though maybe not as many as in today's system. And you're also forgetting the old people will die off, just not as fast as today, and not from old age: instead, they'll be dying from accidents and murder. We already lose a LOT of people these days just from car accidents (30k/year in the US alone last I checked).