My DD was a four year member of the Spirit band. Went to auditions, they had a sax there for her to use. Once she made the band, we sent her sax to her from home. While it is nice to have your own instrument to play at tryouts, it was not necessary (this was 2018. She had enough stuff to keep track of, without a sax kicking around their room, until she A) made the band and B) decided that she wanted to do it.
All of that said, it was one of the best things that happened to her. Gave her a friend group immediately, and afforded her LOTS of travel opps with the football team. Went all over the country, and to a couple of bowl games. Also, as parents, it is a nice perk, cuz you ALWAYS see your Cadet on TV, if you watch the games. Most times, during the game, but almost a guarantee when they sing at the end. SING SECOND!