If that happens, the web as we know it would cease to exist. Without a legal recourse to stop plagiarism and stolen content, people who are actually creating new content stop completely and move into other areas of work. Websites that produce original and unique content close up shop. Instead you're left with a bunch of low-quality rip off sites that have nothing original of their own. Then it the entire web stagnates over the years as very few new things get added to the net as a whole. And that's just the effect on the internet, that doesn't take into account real world publishing.
I wish people would consider all of the consequences of these things before making statements like that. I haven't even begun to consider the consequences of eliminating copyright completely and just from what I can come up with off the top of my head makes it a non-starter.