In most large cities, there is not a single government which has a monopoly on public schools: there are generally multiple individual school districts which each try to compete for the wealthiest students. That results in some school districts being more amenable toward a focus on gifted programs and some being less so. School boards are subject to elections, which does mean that the priorities of the schools are not homogeneous.

Of course there are lots of layers of laws and bureaucracies above school districts that can apply curricula or regulations to temper this, but unlike state governments, where representatives are elected on a slate of issues and tied to political parties, school boards are elected on just 1 issue: how are they going to run the schools.