The problem is
that she'd not be able to be President for a few years.
However, they really should scrap that "old blokes only" bit of legislation just for her!
Paris for President!
Seriously, what's the worst that could happen? She's enjoyed herself all over the world- so knows that there are places outside America. America is in the middle of a financial crisis, a huge upsurge in Orwellian government activity and two wars, so it's not like she'd be able to make it any worse. She's probably also getting a little sick of people following her everywhere so she'd be against all that surveilance crap too!
Plus she'd get the vote from men (because she is pretty hot. And rich. And female.), women (to have a female President). The poor would love her as she's in More or whatever they read over there and has better hair than Barack or his walking dead opponent. The rich would love her because she's rich. She's NOT managed to collapse oil companies (unlike Bush)- in fact her named products seem to be doing pretty well (in that even I've heard of them).
Paris icon because why not? She seems like the best choice from the bunch!