Because their brand CAN be diminished if they start accepting more students. More students need more professors, and it might be hard fighting over who gets to hire the best professors. It might also change the student community. I go to a university that is considered prestigious in my country, and what I like the most about it is how it's so easy to find incredibly smart people on the campus, with which you can have great intellectual discussions. If there were more people, it could be harder to find who these great people are.
It's a Brazilian public university, which means it's free, and while recently it was created a quota for black and public school students, the majority of students is accepted in a completely color, name, cultural blind manner.
The university system has created a surplus of people with phds who are qualified and intellectually capable of being university professors. There are a lot of good articles about how the job market for those wanting to become professors is terrible.
