Why is phenyl shift preferred over methyl shift in cumene hydroperoxide reaction?
Despite the mechanism shown in your question, which is commonly used to depict a phenyl shift, phenyl shifts occur by a slightly different mechanism.



Phenyl shifts do not usually happen by the normal 1,2-sigmatropic "hop". Instead, the phenyl group shifts by more of a "walk". It's not really a sigmatropic rearrangement. First, one of the $\pi$-bonds in the phenyl group can attack the electrophilic center. This leads to formation of a spirobicyclic intermediate where the cation is delocalized throughout the rest of the ring. Then, the three-member ring breaks open at the expense of a carbon-carbon bond to rearomatize the phenyl ring and form the new resonance stabilized cation.