With tens of millions of impeccably natural-born citizens being anti-American, this strategy doesn't seem to be very successful. I would not be very surprised if a greater percentage of naturalized citizens have a strong attachment to America than native-born.
I'm not saying this wasn't their intent, just that it doesn't work anymore.
I'm not sure things have really changed that much.
The Framers of the Constitution held a discussion of this when they were talking about citizenship qualifications for Senator and Representative. Someone commented (I think it was James Madison but not sure without looking it up) that the real danger was not politicians who had been born abroad, because the people would keep an eye on those. The real danger was native-born American politicians being secretly bribed by foreign interests.
Excellent comment!