It is clear that the intent of this natural born citizen clause was to prevent someone who was born and raised abroad and who has another country, so to say, from ever becoming President. It is obvious from the other requirement, which is to be 14 years a resident within the US.
So you say. To me it seems clearer that the intent of the residency clause is to ensure a citizen must have ties and stakes to the country beyond the technicalities of citizenship. And the purpose of the natural born citizen clause is to prevent a foreign carpetbagger from being eligible to be President.