While it seems wonderful that celebrities or the wealthy would personally underwrite schools, this sets a terrible precedent.
First, there is a gross underinvestment in American education across the entire system. Having a few individuals step up when they can, while laudable, does not even begin to address a nationwide problem affecting thousands of schools and tens of millions of students.
Second, the US already suffers from the highest inequality among all the richest nations. This inequality is driven by tax policies that favour the wealthy and social policies that make upward mobility extremely difficult. This inequality is reinforced in the education system: rich kids go to great schools in safe places with abundant resources. Poor kids go to overcrowded, understaffed schools with the most meager support systems.
Privately funded schools may provide needy students with exemplary educations and produce world class scholars, but in effect, it is like an educational lottery system: a lucky few (miniscule few) hit pay dirt, while the vast majority are forced to go without. This is no way to go about fixing the problems in the American education sector.
The countries that produce the best student testing results (think Finland, Singapore, Canada...) do so because their students perform strongly AS A GROUP. The scores of their best performers are not dragged down by masses of underperforming students. This high educational achievement provides the foundation for a solid middle class, less crime, and so on.
No one should be celebrating the rise of celebrity schools. It is a mark of a failed system when a tiny number of the uber rich try to plug a few holes in a dam with millions of holes.