The GPL, in particular, goes further than just refusing to exercise your copyright over a piece of software. The GPL restricts the usage of your software, most notably by forbidding its use as part of any proprietary software. Without copyright no one would have to respect that restriction.
The situation you are describing is closer to a project with an "unlicense," e.g. SQLite, which explicitly makes the project public-domain and places no restrictions whatsoever on its use.
I don't believe that software should be subject to copyright so I put the GPL on my code to protect it from those that do. Fight fire with fire, eh?