Companies already avoid asking about marital status or children etc, this could easily be added to that list.
In other words, there is a signaling and counter-signaling mechanism here. An investment banker saying they went to school in Philly is expecting you to understand they went to Wharton, and the only acceptable clarifying question is something like "oh, undergrad or for your MBA?"
Asking me not to say I went to an Ivy on my resume is fine -- I can disclose it in 50 other ways that will be obvious to the people who care and much harder to censor.
Instead my practice is to literally not look at people's resumes. This isn't perfect -- some co-workers will choose to ask about a project listed on the resume they are interested in, and I don't think that's a horrible idea usually. I simply don't like the assumptions I start to generate when I read people's resumes.
Anyway, school names tend to be worth vastly less in an interview than getting to that point. Face to face Ivy grads are better than average when selected randomly, but because of the selection effect people at elite institutions often get a negative bias to Ivy grads. https://en.wikipedia.org/wiki/Simpson's_paradox
PS: You see similar things when look at people from say MIT by SAT score you would find the lower scores tend to be better indicators than high ones. Which is the same issue, people with low scores need other factors to get into the door.