It really depends on the outcome of IvX. I suspect that Storm's leadership will take a hit because she tried so hard to work with the Racist Xenophobic Slave-Owners, but it didn't work. They still had to go to war in the end and her diplomacy failed. However, she still inspires a great deal of support among the X-men. I think she's definitely the most qualified to run the school in the absence of Charles Xavier (who may not stay absent, given the events of Uncanny Avengers).
I can still someone like Emma Frost taking over the day-to-day operations as well. Again, that really depends on how IvX pans out. Given her deceptive tactics and her allegiances with Magneto and the Hellfire Club, I think that's a long shot at best. I suspect that if Emma is involved with the Xavier Institute or the X-men in any capacity, it'll be limited. I think if word gets out about the massive psychic deception she employed in Death of X, the X-men won't trust her enough to run the school. That said, they have trusted her before so she can do it if need be. Personally, I'd like to see Emma Frost in this role. I'd rather she not become a villain again, which may be the course she follows after IvX. But I'd be okay with Emma or Storm.
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