you are wrong.
if being a citizen was enough, as it was for all other Constitutionally defined positions, they wouldn’t have used a different term for POTUS
It definitely means something and frankly, if the founders didn’t define it, then it should be used in the strictest sense and include every possible exclusion as I see it only benefits our nation from the threat of foreign allegiances. The definition is only needed by those seeking to usurp it.