Hmmmm... nice thought. But then the artists would need to be able to practise their art for free as well. And as long as a musician needs money for instruments, a rehearsal room, recordings, promotion and distribution, he will need to sell his art in order to continue - even if he doesn't make any profit himself, but only uses the money to compensate for his expenses.
Unfortunately, this is the point where he begins to depend on others: be it a label that wants to tell him what music to play in order to get better sales, be it some enthusiast who sponsors him but in return maybe expects certain things and wouldn't continue sponsoring the musician if he chose to play some different music all of a sudden...
And if a musician would only record stuff at his own cost and make it all available for free, then only the better-off could afford to make music, and it could be damn hard to get access to somebody's art because without some good means of distribution you might not get it where you live or maybe you just wouldn't know it exists at all.
But sure, the thought of walking into a museum or an exhibition and looking at some beautiful paintings or sculptures whenever you want and without having to pay... *sigh*
I think you could even make much of our culture available to the public - the sad story is that people in total tend to be a bunch of selfish, careless, irresponsible, stupid, uneducated and destructive assholes - if you put up a famous painting for everyone to access (no museum, no security, no personnel = no cost), some shithead would be likely to steal or destroy it, unless of course one of those brainless graffitti sprayers had sprayed his childish tag on it first. >
Likewise, if all music was legally available on the internet for free, but people would have the option to pay as much as it means to them, chances are that 20% would pay something whereas the other 80% would just grab all stuff and leave the musicians out in the cold.