One of the most attractive aspects of imposing Mayoral control--vice school board oversight--via Mayoral Academies or the like is that it is a vehicle by which a school can start fresh by cutting through the red tape and other problems currently hamstringing innovation in our schools. Further, it puts one person--and a visible one at that--"in charge" and accountable. But it's not a panacea and some of the very criticisms currently levied against politicized school boards could eventually be applied to mayoral-controlled schools .
For his part, eduwonk Fred Hess thinks mayoral control can be effective in urban districts, but also warns that it's a model that doesn't address the root problem of school district composition and the delivery of services. He and Olivia Meeks advocate for "organiz[ing] schooling around function rather than geography" in an interesting paper that delves more deeply into the issue. Have a read.