What role should the government play in art?

Most likely none if they are not financing it. If a person is taking some government endowment or public finding, then it is just like getting an allowance from Mom and Dad, and they rate a "say so" on what you are doing with it.

education in the arts. Art education in elementary and secondary schools, be it in calligraphy, music, etc. etc. etc. has sometimes led to careers in diverse trades and professions, from music to professional painters to actors, forensic artists hired by the police to solve crimes, etc. etc. etc.