Your point doesn't speak to the issue. The founders came forth with an idea of general principles. No one ever suggested that it would be infallible, but the thinking behind it is that it would improve probabilities.
The practice of Marrying Foreign Royalty into other Royal Families was well known at the time. The intent was to gain influence in the affairs of other nations so as to look after the interests of the Origin country.
By requiring people to be the offspring of American citizens, the only country who's interests would be looked after was our own. Not so with people merely born here, and such issues were made manifest with all the troubles which Madison had with Brits Pretending to be Americans during the lead up to the War of 1812.