That would seem reasonable in this day and age - but absent a Constituional Amendment, we are talking about what the Founding Fathers understood at the time they wrote the Constitution. The father would have had to have been naturalized prior to the child's birth.
I disagree, mainly because the Founding Fathers were composed of many a British immigrant (including Irish immigrants). Rejecting the British crown to live in America was what defined this country. Shanks v. Dupont reinforces this idea by noting that those who were native born in this country but adhered to the United States were considered citizens and those who adhered to the crown were considered British subjects. Naturalization laws have been somewhat arbitrary as to length of residence and other requirements. At that point you're getting away from the natural character of allegiance.