The HD being the "face" of the band program is incredibly important, even if only within the confines of the school district. If anyone wants to get in touch with the band program, for any reason, it's not the AD they're going to call. The HD may delegate some of that responsibility, but it will all filter through the HD's office at some point.
Given that you're still in college, perhaps you should stop arguing with the people you asked advice of and just listen. You're on the outside looking in.