My thought is that this is very much kid dependent and more about what the individual wants to pursue during high school years and how focused they are on their goals.
We have 3 kids, all very involved in music. Husband is a freelance musician and with a degree in music education.
First two kids were reasonably happy with our public high school, music subsidized with lessons and youth orchestra. Oldest is a performance major and probably practiced 1-2 hours a day at most during high school.
Youngest was miserable at same HS. Involved in 2 varsity sports, lessons and 2 pre college music programs outside of school and hated the school music programs. In retrospect, probably torn in too many directions and with nothing at the level he needed. After sophomore year, he asked us to transfer to a performing arts boarding school. There he completed HS, practicing on average 4 hours a day (probably the maximum healthy amount on his instrument) with high level teachers and similarly passionate peers. This worked out well for him, he was accepted to high level conservatories and is currently entering his fourth year. Very happy with his choice.
Having said all of this, in my opinion this level of commitment and hours of practice are not necessary for music education applicants. As @murray93 states above, the audition level is not as high. Music education and music therapy applicants will benefit more from a breadth of music experience in high school: genres, instruments, voice and teaching/coaching.
Regarding changing schools, it sounds like your son is reasonably happy where he is. In our experience, reasonably happy was the norm for our kids. (If some parents have the secret to complete happiness with their teenagers…feel free to share!) I never thought we would pull our youngest out of the local school and move him across the country. But he was not just unhappy, he was beyond miserable knowing he could not get where he wanted to go.
I second the advice to explore the public universities in your state (or the state where your son would wish to live and work) For music education, this is definitely the most efficient path.
Best of luck!