A few comments (that will go around in circles…lol). My final point is really to work methodically and slowly through this, collecting data…until the answer is more clear.
1.) Talk with her private teacher about this. She should be a great resource.
2.) Talk with the music school about it. What is their policy? And, why? If it has worked for years…could it possibly work for your kid?
Some schools do this…no teacher assigned…and they are still in business turning out great musicians! However they should have a clear philosophy and process. Also…I think that they should have a robust faculty. And, then you need to decide: does this work for my kid’s personality or not.
3.) Talk with the head of the voice dept, if possible. Why would they place your D with one teacher or another? What if it doesn’t work. Most schools allow changes and really do try to help students.
My D UG teacher was particularly good with certain voice types (mozart-type voices). I would have had no idea about this. We may have picked a different teacher not understanding this. A good faculty may have more insight on your kid’s future (than you can glean from website searches).
4.) I understand that particularly for instrumentalist the teacher is often “everything”. My comment is only “opinion” but for young vocalist (only really coming into their voice in the last year or so) it is harder to know what you need. However I do understand that your D has had some very good instruction with a U faculty teacher so…she may be more advanced in understanding her needs. But my D put herself more in the hands of an interested teacher…at a well-known program with a big faculty. Her focus was a music school with flexibility. The teacher was important but not more important than some of her goals. So what does that mean for you? I don’t know. I just want to say…if my D made her “whole” decision on a teacher…and did not look at other elements of the program…she may have been “unhappy” and not grown.
5.) I would start from a position of “curiousity” as opposed to “judgment” on that process, if possible (and I’m not saying that you are judging!). But I get that is can feel “negative” and “scary”. If that persists, then it may not be the right school. Something more certain could defintiely be a better fit.
I hope this helps in some way.
Edit: All communications with teachers should go through the kid. With “administration”, I have a more mixed feelings…thinking it’s OK for a parent to ask some basic questions…like what’s the process of teachers at your fine school. Idk, I’m sure you’ll figure that out!