That's not a caste system. Please read: https://en.wikipedia.org/wiki/Caste

It's a class system, but nearly all Americans insist that they are middle-class: upper middle class, lower middle class, but definitely middle-class.

https://www.investopedia.com/terms/m/middle-class.asp

I have never been asked to put my parents occupations or net worth on a resume, or been asked it in an interview.

You don't have to. It comes up with your universities, your hobbies, your zip code, even your name. That leads into what jobs you get, how much money you earn, and now what position your kids are in.