The reason the kids in private schools get a higher test score is not because of the private school itself per se, but because the parents that invest in the kid going to this private school take a much larger interest in their kids, and their kids school work and making the grades. One does not equal the other.
Lots of kids in public school being raised by single parents/ grandparents/ foster care, and parents that just don't give it any thought, that don't go any further than the kid making it to class, and calling it good.
Building a $100,000,000 school does zero for a kids education, absolute zero. 60 years ago a kid was taught in a one room school house, and learned more than our kids do now.