This sounds like a great idea because besides vetoing the religious freedom bill (which btw every Republican candidate for Governor except Al Melvin supported a veto of), Brewer is just a terrible, terrible woman who would get pounced in the primary. Though something tells me she might go after McCain's seat now if he does retire in 2016. She's shown she loves her power.
Another potential candidate also seemingly declined in Steven Seagal, so there's that. I don't think a Benghazi conspiratist is much better than an old woman who loves her guns and hates her gays and immigrants, anyways.
FWIW, Brewer also got the Medicaid expansion at pretty large political cost to herself.