This is not a law of nature, it is history as it unfolded in the twentieth century. We don't know if that'll continue to hold or not.

Yea, but it’s still an open question when or if this stabilizes. A global population of between something like 100 million to 10 billion could sustain an advanced technical society capable of innovation. But, where slowly oscillating between say 1 and 2 billion people would be fine, regular massive population crashes could represent a great filter which generally prevents interstellar civilizations.

And the more a country develops, the more resources they consume per capita. One individual in a developed country consumes orders of magnitude more than one in a less developed country.