This assumes the rate of deaths stays the same, that we can't automate certain processes and that we also maintain the current economic model which requires gro

This assumes the rate of deaths stays the same, that we can't automate certain processes and that we also maintain the current economic model which requires growth to sustain retirement funds and government services. “Healthy birthrate” is entirely dependent on the underlying structure of that society. Alternatively, we could adjust and actually require less people over time. I'd argue that in many ways we've reached the point where a growing population is not healthy at all.