Simply stop funding schools based on local taxes, fund all schools equally based on federal and state taxes. Many problems solved.

Because private industry would not build schools for those students in depressed and poor neighborhoods, even at the guarantee of the general fund of the school that was there, because most schools in the US are operating at a substantial loss to their direct income from school / property tax.

Its part of why "bake sales" to fund schools are so common in many depressed and poor areas. Its also why schools are so strongly incentivized to seek funding for sports, sports programs, and sports arenas. If you can build a fancy stadium on a state grant it can bring in supplementary income to keep the power on for general ed.

Private enterprise would only be interested in building schools for poor kids only offering public dollars if there were profit to be made from said dollars, which is innately more inefficient than a public school that simply operates at, or better, under cost - especially when that general income is coming from direct local residents.

The unpredictable nature of school funding would then be a pretty big problem, and the results for students who choose wrong, have the schools in their neighborhood all but defunded / can't afford to commute to a better school would also be bad. It would basically be the existing school funding issues, on steroids.