What is band?

I teach a graduate class at the University of Bridgeport in Secondary Music Methods.  These students are generally musicians who have decided to get their education certification.  Some students are current teachers working toward their masters.

We have had many discussions trying to define what band is.  We have spent many hours discussing Peter Boonshaft's books, discussing shortcomings of a traditional band program, and what a program should look like.

I posed this question: should a HS band student be able to play out of a Level 1 piano book?

Now--many of these students remembered the frustration of keyboard exams in music school and also lament that the piano has become a much less important instrument (everyone has been asked "do you want my Aunt's piano?").

The question, I think, gets to the heart of "What does it mean to be a good musician?".  What do you think?  What should band look like?