There likely is another reason, I agree. But, the stipulation that it be the father was discarded in the late 1890s, I believe, and was replaced by “a parent”.
The loophole in the Constitution was put in place for a single person, by the way. Every one of the Founders met the requirement that they were born in what became the United States, save one: Alexander Hamilton was born in the Bahamas.
Actually none of them were born in the United States. They were all born within a British colony subject to George III.