Wouldn't eliminating of copyright render the GPL unenforceable? I'd imagine you'd have to fall back to a BSD-style license, which (according to the FSF) is less-free? [not agreeing or disagreeing].
Pretty much all FLOSS licenses would be unenforceable. They only work at the moment because copyright prevents works from being distributed without permission, and the only permission you get for distributing such works is through the FLOSS license. If you don't adhere to the license terms (e.g. providing source, attributing authors, whatver...) you have no other way to distribute without breaching copyright.
So BSD licenses would be just as pointless if there were no copyright.
It was written to turn copyright on its head. While it's true that eliminating it would weaken the GPL, it would also be less necessary, because freedom would be the default.
That said, I think RMS wrote an essay talking about why certain 'reforms' could be dangerous, in that we might end up with a weaker GPL but little else to show for it. I can't remember it clearly enough to find a citation for that right now, though.