Fistful, the "brain drain" you describe affects states in the US probably more than it does second or third-world countries.
Example: Wisconsin has one of the largest state-run university systems in the country. As a state budget item, it ranks near the top.
But studies have shown that an imprortionate balance of graduates leave WI for states that offer better jobs, salaries, and so on.
Let's look at India's Institute of Technology, the equivalent of our MIT.
IIT doesn't have to draw from hundreds, or even millions, of applications. It draws from hundreds of millions, and only accepts the best. At that, IIT can afford to pick and choose.
On a personal and purely anecdotal level, though, I've found that US companies who bring stateside graduates from IIT tend to discard them quickly when the jobs run out. Maybe it's a cultural thing, or maybe it's merely perception: do you want your tech support person to be able to speak English?
"I wonder if there's not a much larger phenomenon occurring, in which the "better sort" have been clustering in America for centuries, leaving the rest of the world to corrupt leaders and to citizens less vigorous, less enterprising or just more tolerant of poor government and poor social conditions."
But, to wonder about "clustering" better sorts of people here for centuries: that can only imply one of two things:
That, for centuries, individuals, families, or maybe even entire even entire monarchies have said, "hey, man, let's get our asses, our money, our women, and our children over to the USA as soon as possible. I heard that there was this Hitler dude coming in like 200 years, so let's get our butts out now."
Or that, through some secret plot, the USA has been actively recruiting entrepeneurs since the founding of our country.
Actually, Fistful, I think that those who have power and influence in their countries gain by staying there. And that, those who come here, come here with a hope and a dream that cannot be fulfilled in their home countries, because they are without political power.