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.