Well, of course there is a reason. It's very simple. Growth rates are much lower in richer countries than the rest of the world. As an economy matures, the growth rate slows down. Therefore there is a a tendency towards equalization.

It doesn't need to become exactly equal. The gap just needs to shorten. And it does, at exponential speeds.

Already the average GDP in the West is only twice the worldwide average, this only shrinks every year.