Copyright is the foundation of all FLOSS licenses, from GPL to MIT. You might know that already, but that's a sharp double-edged sword you're swinging.
With the GPL at least, its major clauses are aimed at restricting software from being incorporated into closed systems. I don't know if eliminating that control was what the GP had in mind, but it would be one of the perhaps-unexpected effects.
See also: Licenses that prohibit use for military purposes or other things the authors consider undesirable.
Without copyright there wouldn't really be "closed systems" any more --- sure, you might not have the original source, but it also becomes legal to decompile and publish the results --- and as the cracker/hacker/security community has shown, source isn't mandatory for doing interesting things with software.
If anything, the loss of copyright would cause a great advance in reverse-engineering technology --- and also attempts at defending from it. IMHO not such a bad thing after all.
Flipside: copyright is a human construct. So is the GPL and concept of copyleft. It is possible to eliminate one thing (say, overbearing copyright) and protect another. Rather than creating a class of works under license which cannot be constrained, it might be possible to create a set of works under law which may be designated with equivalent protections.
Or find other means to the same ends as the GPL: protecting the three freedoms laid out by RMS.