Nushi, because there is some conflicting info on this thread, you may find this report from the Assoc for Univ and College Counseling Center Directors annual survey to be of use. It provides a current picture of the functioning of a broad selection of Centers with stats broken down by size of institution. There is even a list of participating schools, so you can check to see if your Univ is a respondent.
https://www.aucccd.org/assets/docume...blic-apr26.pdf