1) She's black Yes, I'm pulling the race card. But hear me out. Obama, perhaps out of all his predecessors, has suffered virulent, baseless criticisms about his ideology, race, religion, and history. No other President has ever been called anything close to a "secret commie moslem". There are no films accusing past Presidents of trying to undermine the eminence of the United States for the sake of evening the global playing field (i.e. "2016: Obama's America"). Imagine what Storm would have to go through. Even though Storm was born in the definitive American city, New York, her varied history would likely fuel barbs against her character and the team. That brings us to the second point.
2) She has a checkered history Would you vote for a person who is worshipped as a goddess in a third world country? The very fact could open her up to policymakers and pundits doubting her ability to lead democratically, regardless of whether colleagues and (comic fans) know the truth (she's awesome). Her career as a pickpocket could easily be dug up and scrutinized past reason. And what of her marriage to Black Panther? Doesn't her marriage call her loyalties into question? Yes, the marriage will likely end soon, but still, it's another chink in the armor.
3) She's an integral X-Man Although X-writers may not bless their pages with Storm as often as they used to, she's still an iconic and crucial member of the team-cum-organization. Perhaps she's too close for some people's taste. She may have been a Cyclops critic during AvX, but perception holds greater weight than truth.
4) Her marriage is crumbling The love Storm and Black Panther had could not welcome the rigors of DoomWar and AvX. Operating on a lower profile may give her sometime to heal after the fact.
Thoughts? Agree? D I S A G R E E ? ?
p.s Havok may not have been the most obvious choice for leader, but there is nothing in his history that would make him open to criticism quite like Storm. No one remembers Inferno, his time with the Brotherhood can and will likely be chalked up to "covert ops", and, despite jibes saying otherwise, he is a great leader, with a resume to boot.
EDIT: It's interesting how Havok has been chosen to lead integration efforts between mutants and humans. Havok and Polaris left the X-Men early on to lead normal, productive lives. Had it no been for the X-Men, Havok might have earned his doctorate and shared a life of research with Polaris. Having Havok act as the public face of a PR effort like Uncanny Avengers makes sense given the life he's led before "War of Kings". Cyclops was the one most committed to Xavier's dream, but never had the chance to live amongst normal people, human or mutant. Xavier had decades' worth of life experience exploring continents before leading a paramilitary/outreach/education organization. Perhaps living in a bubble (combined with recent plans for the character) did not prepare Cyclops for closing the human-mutant gap. On the other hand, it seemed like Cyclops was on the right track in "Astonishing X-Men". Hmm.