No, actually, the more affluent a nation, the lower its birth rate. 3rd world countries tend to have very high birth rates, like Mexico, the very subject of this thread.
Are you saying that 19th century America was poor? We were the richest nation on the planet. Yet our birthrate was phenomenal.
Moreover, name one "affluent" nation in the late 20th century that had real reason to be optimistic.
Affluence in the 20th century west has come with a real fear of growth. The "isms" of the 20th century put fear of life into us. Consider fascism, communism, and the new French philosophies -- each with their own "isms."
The west became afraid of its own shadow. The correlation of wealth to birthrate is only partly related.
So the American elites, and the western globalists have decided to replace our flagging growthrates with immigration, regardless of the cultural impact.