Public schools are public schools. They're more or less compulsory and are just meant to try and get you to a point where you can contribute meaningfully to the society.

Princeton is very much optional and is a school for future elites. They're supposed to produce CEOs, politicians, and Nobel prize winners. So the standards should be different.

Of course, expectations are a part of the problem. Many kids go to Princeton or Stanford or MIT because they had wealthy parents who really wanted their kids to go there. And many of these kids are mostly interested in computer games, weed, and the opposite sex. A combination of unmotivated students and high academic standards lead to predictable outcomes.

Public universities (what Americans call public schools in the context of higher education) are optional to the exact same degree as private ones. In other words they are all schools that you apply to.

They also produce more "elites" than "elite" schools do if you go by executives at F500 companies and politicians.

Are we going to pretend that Berkley, Michigan, UNC-CH, UVA etc. do not produce world class educations from world class people?