Otherwise, private schools can be as much of a mixed bag as public schools. Some are phenomenal and produce great thinkers and citizens of the world. Some turn out “graduates” who can barely read at a 5th grade level (private schools in Texas are very lightly regulated, not usually required to test students based on national norms though many do, and some are just fly by night operations meant to bilk desperate parents).
You make the assumption that testing for "national norms" means something - and that public schools do better with testing to national norms. I have seen people who can test well but have no capacity to really be a thinker (nor get very far) and vice versa.
One of the things I wrestled with when we were given DS's scores that stunned us was - what exactly do I consider an education? How/where do we want that educational setting to be? And that is going to be very personal - for some families, it is to be "best at every academic level", for some, it is "must go to ivy league/research", for some, it is to be at least at the "national" level for each grade. So schools (and to some extent, the teachers) will usually reflect the collective values of the parents - although public schools have to figure out how to combine the collective parental body's values with the bureaucratic dictates set by government.
Note - not all Texas parents are focused on football, and Texas has some great schools and great universities... all states will have pockets of poor schools and good schools - public and/or private, even in the highly touted MA (my husband went to a "highly regarded" public school system in MA, and we would never send our children to a school system like that. ever).
