I think caution is most warranted, but I also think it's likely that SpaceX will become a real-life Weyland-Yutani Corporation (i.e. "The Company") of Alien and own space. But I'll be long dead before that plays out.
Musk isn't a natalist. The global population is going up. And yet, he complains about not enough births. Because he is a white supremacist. He wants white people to outnumber other races. The current state of affairs would be satisfactory to him if he were merely a natalist.
The population is very hard to count, believe it or not. In many places, the birth rate is well under replacement and in the others it's dropping quickly. Furthermore there's widespread fraud and deliberate miscounting which also makes it hard to really know.