The usually clever (years ago, anyway) Simpsons writers, in bending over backwards to mock the governor of their home state, made absolute asses of themselves. On two counts:
1) They never explained how Mr. Schwarzeneggar could become president. It is generally assumed that rules are the same in the Simpson’s universe as they are in ours, unless we are told otherwise, and such a large, unexplained hole bothers people (like me), and
2) They already had a well-established parody character of Schwarzeneggar, named Ranier Wolfcastle. Why couldn’t they use him? Too subtle?