There is also a fact of life called K-extinction.
When the population density of any species reaches a genetically coded value, the population experiences an extinction event.
K-extinctions come in two forms - determinate and indeterminate.
A determinate K-extinction is predictable in form. An indeterminate K-extinction can take a variety of forms.
If you want all the detail, research and maths, read ‘Sociobiology: The New Synthesis’ by Edward O Wilson.
A good book of its time (1975, and which I have read), but things have moved on.
As mentioned, many countries have less than sustainable birth rates (as they become more prosperous), and it is unlikely that the old will inevitably live to greater ages. A more realistic proposition, as proposed by Hans Rosling, is that we will probably level out - even if this is still too high for comfort - especially when we all need to be consuming less and this just doesn't appeal to the expectations of many. Like so many seemingly wanting what many in the USA have, and which is just not achievable. Which is why we need to change our love affair with capitalism into something far more realistic. Not to mention the damage we are causing to the planet and all other lifeforms.