At Stanford, faculty are prohibited from proctoring. So there is no professor or grad student that sits in the exam hall with the students while they are taking the test:

"The faculty on its part manifests its confidence in the honor of its students by refraining from proctoring examinations and from taking unusual and unreasonable precautions to prevent the forms of dishonesty mentioned above."

https://communitystandards.stanford.edu/student-conduct-proc...

A professor or grad student walks into the room every 30 minutes or so just to make sure everything looks okay. They otherwise sit outside the exam hall so you can ask them questions, ask to go the bathroom, etc. But it's up to the students to police each other and ultimately themselves.

There are definitely other universities in the US that have this policy, but I would say it's more the exception than the norm.