I object to your use of the word privilege in this context. The problems in poor schools in the Houston school system are in large caused by elements of their own communities. Politicians representing these poorer communities are notorious for preventing reform (Sheila Jackson Lee for one), or even enacting policies that are counter productive. They, along with the teachers union and community activists and leaders, also make it damn near impossible to fire, suspend, or constructively reassign teachers from underperforming schools in these communities. They seem hell bent on making sure these schools continue to underperform.
In addition, any talk of encouraging competition in education, or providing these communities with additional educational options for their children, are called racist, or a "war on education." So, they wont improve the system they have, they rabidly oppose any alternatives, and they definitely don't want to take responsibility for how their brinkmanship and inflexibility affects their community.
It is one thing to recognize and then try to make adjustments to compensate for perceived societal inequalities. I support this as rational and responsible behavior. Its entirely another thing for political and community leaders to create inequalities in their own communities that are destructive to the educational potential of their constituents, thereby perpetuating the cycle of poverty, and then blame it on something or someone else.