so I'm not sure that their recomendation would have any artistic merit.
Major donors have some sway, and the more major they are, the more sway they have.
This isn't about winning the Met Audition, where the best performer should win. This is about selecting students that can benefit the most from formal music training. You do what you can do to be one of the selected.
Having a Patron helps most in the situation where it is between Student A vs. Student B, where Student A is a little better. If Major Donor wants Student B, then the school will do what it can to not upset Major Donor. It becomes a more dicey issue if Student B is not really qualified. Then it is an issue of the school relaxing its standards, and that is not in the school's best long-term interest (graduating students that perform poorly).
Even if Student A is a little better, no one really knows whether Student A has a materially higher likelihood of actually being better. Thus selecting Student B is within the "margin of error", and not a real compromise of standards.
The issue is not that much different from a student coming from a wealthy family. A child from a family that can afford whatever school Student A wants to go to has more options. At an unaffordable school, Student B never had a chance compared to Student A.