The competitiveness of each school differs depending on where you apply!
Definitely don’t audition 20 schools and mostly likely once your daughter finds out places or programs/schools she is genuinely interested in. She won’t go over 10 schools. And even then: ngl, most people don’t actually need to audition to ten schools, especially if your daughter has string musicianship and great academics; she can narrow down her options based on school locations, class structure, course load, undergrad graduation requirements, the general vibes of schools-- and get down to fav 5-7 schools to audition at most.
Auditioning more than that amount of schools can exhaust you and your daughter and spend a lot of money and time on applications you def don’t favor as much. Goodluck to your daughter on her music ed adventures!!