I would say that a band isn't a business but a brand is, and most bands, and sometimes even just people in general, seem to have a brand of some description these days.

I think most artists don't have the greatest business sense which is why managers, agents, etc... exist. It's not just the music industry either, I think everything you've said is applicable to most if not all of the arts.

I don't think art and business are opposing forces, just different forces, and I'm sure there are some people who are good at juggling both.

I think if I was to ever get really serious about making a living from art/music I'd definitely need someone to take care of all the business stuff because I just don't have the head for that.