Before copyright, people still made a living from music, books, art, etc. It was just a different model, patronage was common, the modern equivalent is probably something like kickstarter. Even under the current system, most artists don't make a living straight away, they have to gain recognition whilst doing something else before it becomes their full time job.
And this business model really isn't as alien as you might think, many industries require deposits, milestone based payment, etc.
However, despite having been corrupted by greedy entities into a parody of it's original purpose, copyright has undeniably been beneficial to western culture over the past 100 years.
I believe there will be a grand bargain at some point, where citizens will be asked how long a copyright should last for, and an agreement will be reached. "pirating" will become something that is seen as morally wrong by society (at the moment most people see it as "a bit naughty" at worst).
How long it will take for the corporations to give up on copyrights that last more than a human lifetime is difficult to say. It is surprising to me that americans are willing to put up with a system which means that the only video of martin luther kings i have a dream speech will likely never enter the public domain.