As a professor at the University of Rochester in New York (private university) when I taught intro to programming to engineers with ~150 in my class, grading was done by a team of graduate student TAs that I supervised. I wrote the exam, I taught the class, and I supervised the grading giving pretty explicit instructions on each problem how to grade it and grading them all together so questions could be addressed in real time.

Essentially it was me grading the exams, but supervising a team.

The remarkable thing to me was there were no foral checks and balances on either the quality of my teaching or the quality of my grading. This was true the entire 8 years I taught there, and I think is completely typical of US higher education.