George Washington was concerned about just that, seeing as how he took the advice of John Jay upon the matter.
Recall the letter to George Washington from Jay:
New York, 25th July, 1787.
Dear Sir,
Permit me to hint whether it would not be wise and seasonable to provide a strong check to the admission of foreigners into the administration of our national government; and to declare expressly that the commander in chief of the American army shall not be given to, nor devolve on any but a natural born citizen.
I remain, dear sir,
Your faithful friend and servant,
John Jay
“George Washington was concerned about just that, seeing as how he took the advice of John Jay upon the matter.”
Well, he didn’t stop it, so poor him.
“Permit me to hint whether it would not be wise and seasonable to provide a strong check to the admission of foreigners into the administration of our national government; and to declare expressly that the commander in chief of the American army shall not be given to, nor devolve on any but a natural born citizen.”
This demonstrates nothing. Soil babies aren’t foreigners.