The main problem GPL is trying to solve is to keep code free and this problem wasn't created by copyright. In a society without copyright it would be even more difficult to keep code free.

Copyright just allow you to claim some right over the code you produce. In a society without copyright you would not be able to make this claim so, if you publish your code it will be free, but : - nothing force you to publish your code, you can keep it for yourself and just distribute binary ; - nothing force other people to distribute there modifications of some free code.

Copyright is what allow you to say "this code should be and remain free", the only alternative in the view of the GPL and FSF should be a law who say "all code should be free and remain free" or something like this.

(just to be clear, I'm not a partisan of the GPL but this is my understanding of it)