The real foreign influence that the founders were concerned about occurred in 2008 when a non-natural born citizen was sworn in as President.
The founders correctly restricted the office of President to those who were naturally Americans because they simply could not be anything else. Born here of citizen parents.
They wanted to prevent those with divided loyalties, allegiance, nationalities and citizenship from becoming President.
Children of foreign nationals were exactly who the founders were excluding.
“Children of foreign nationals were exactly who the founders were excluding.”
I can think of no question on which they were unwise.