How do babies learn to talk? By listening to people talk. How do instrumentalists learn to play with a characteristic sound? By hearing a characteristic sound.
In band it is rare for students to perform by themselves and if they do, feedback us usually limited to 10-15 seconds. Performing weekly for a teacher helps them become a more confident and independent player. They also have more time to give feedback, try again and continue to work on a problem until it improves because it is an individual setting.
These fundamentals are crucial for later development and more advanced playing ability.
Method books, because of their methodical nature, do a much more complete job of covering full range, key signatures, rhythms, duets, alternate fingerings and styles than the curriculum in band class allows.
Teachers can meet a child where they are to begin the region band music and help them develop an individual game plan to prepare them for the audition. This helps students learn how to set goals - long term and weekly goals.
While students move through different classes, grade levels and schools, it is possible they would have the same lesson teacher for 7 or more years. Lesson teachers often have a long term plan for each student’s development. Private teachers can guide a student all the way from the first sounds in beginner band through a professional level solo as a senior in high school and they know how to get them from one point to the next.