My husband got a Chemical Engineering degree from Oklahoma State University, my brother in law got Veterinarian degree from same U, our daughter got degree in HydroGeology from University of Texas, and they all do QUITE WELL! I think your degree that you get is more important that which school you go to.
OSU...has a great Vet School.
You are correct for the most part but there seem to be some fields that are restricted to the most elite colleges. Every member of the US Supreme Court went to Harvard or Yale Law School. I can’t believe there isn’t tremendous bias here. There are other top notch Law Schools.