I keep coming across these misconceptions, so I thought I would put some facts in one place.
The music industry is run by greedy, fat cat major labels.

Maybe this is partly true, but I rarely listen to major label music myself.
Since the late 70's there's been a wealth of independent labels, but they are also targeted by free downloaders.
Some of my favourite music comes from:
R & S Records Shop
Mute.com: Home
Sonar Kollektiv

Not a greedy, fact cat in the house as far as I'm aware.

Recorded music can be paid for by live shows.

Well it already is for the big name acts like Madonna and Coldplay, and for young indie bands who are prepared to tour for much of the year in poor conditions and for poor wages.
But a lot of amazing music is produced by musicians who can't or wont tour:
Apollo: Atmospheres & Soundtracks: Brian Eno: Amazon.co.uk: Music
Gorillaz: Gorillaz: Amazon.co.uk: Music
Martes: Murcof: Amazon.co.uk: Music
The Remixes 1997-2000: Jazzanova: Amazon.co.uk: Music
A Meeting by the River: Ry Cooder & V.M. Bhatt: Amazon.co.uk: Music
Music for a Darkened Theatre, Vol. 1: Film & Television Music: Danny Elfman: Amazon.co.uk: Music
Brüder des Schattens - Söhne des Lichts: Popol Vuh: Amazon.co.uk: Music
Koyaanisqatsi: Philip Glass: Amazon.co.uk: Music