Every school is different and what you call an elite program may vary. I know for a fact Juilliard is needs based, for example, they outright say it in their presentations, NEC is definitely like that. Curtis and Colburn don’t count because they are free schools (tuition at Curtis, Full at Colburn), and it depends also on the instrument as well, I don’t disagree. But when you are dealing on the level of Juilliard, where they literally are inundated with talented applicants, getting merit aid is slim, pure and simple. I am sure if a teacher has some student they are high on, they might be able to.
And I am not basing this on a small sample, my son remember is a musician now, and through him have come into a good number of high level musicians who have gone to a ton of different programs. Some programs are better with aid, of course, Rice tends to be particularly generous. The other thing with awards (not to start a controversy), but if a kid represents an under represented minority, that can weigh in too these days.
You also have to look at the total cost of going. Someone listed a 15k award to Berklee, but if you look at the total cost of going there, that isn’t much , the top music schools, however you want to measure it, have total cost in the range of upper tier colleges.
When I talk about top programs it isn’t meant as a knock on other programs, but put it this way, if a program has really selective admissions, can pick and choose literally from among the best in the world, giving merit scholarships is problematic (and again, it depends on the school, there are some top level programs that pride themselves on aid, Juilliard for example isn 't one of them). A program that is good but for example isn’t as competitive because they are a smaller program, don’t have ‘prestigious’ teachers, is going to be looking to try and induce top kids to go there, so they may offer more.
In my son’s case he wasn’t at the level of the kids who already had artists rep, who were winning competitions (someone like that could get merit even at a place like Juilliard), but he also graduated from Juilliard’s pre college program (the year he got in there, they admitted 6 on his instrument, 130 applied/auditioned, just to give an idea of level).
It isn’t that I am trying to discourage anyone, but with music schools total cost nearing at least the 80k range, even a 15k merit wouldnt pay for all that much and their needs based aid is pretty stringent (like many schools, they push loans, these days parent and kids). One thing is true, you never know, if you are a kid from a rural area they may give better aid or if a teacher really likes the kid, but it isn’t common at the level of school I am talking about.
And as with everything, obviously I cannot say with any kind of accuracy what would happen with any student, my sample size while fairly large isn’t comprehensive by any means and YMMV.