There's the real reason the Constitution requires the President to be a US citizen by birth: we don't want to allow candidates to take those elitist trips home. Imagine, for example, if Arnold Schwarzenegger went to Austria! Who does he think he is? Mozart? A celebrity? Un-American? (Question for homework: Why would this not work?)
Note to aspiring candidates: if you want to run for President, make sure you are born in Dead Possum Hole, Redneck State, and you go there for vacation. Alternatively, you can run as a Republican.