That only solves one of the problems and the GP was talking about limited resources which doesn't change even if you make the income/wealth distribution equal.

One person would still need 8 litres of water, a piece of land, food and other essential limited resources.

How do you plan to let all the people have kids with an existing population density of 828 persons per km² without ruining it for everyone?

What other filter do you propose is realistic? Do you think there should be a test, higher age requirement, education background or something?

Clearly, the current population is too much here. Sure it is declining (predicted to be normal replacement fertility rate by the end of 2020) but that will take long time to materialize and then you have government doing something to stop it because failing economy. Why even set your whole structure in a way that requires numbers? This is a perverted incentive and should be stopped.

https://link.springer.com/article/10.1007/s10668-015-9711-5

Optimum world population is something around 2 billion. Not 8 billion and growing.

As a counterargument, we're taking only a tiny amount of land that's feasible to develop, and even less of total area of Earth. Scarcity is caused by concentration of jobs in cities. Where there are jobs and education, there become cities. There's more than enough water to go around, but not energy to desalinate in drier places like China and India. There is a surplus of food in many areas, and most of lacking ones are limited by water.

You cannot speak of an optimum without having decided a target. It's optimum everyone having their own private jet?