Only if distributing software without its source was also made illegal.
WTF?!? No way! (although to be fair I'm not exactly sure what you mean by "use of code").
Companies would still be free to "protect" their code through secrecy: releasing only the compiled version and not the source code
This is exactly what the GPL is designed to avoid.
As you quoted above "the freedom to change the software to suit your needs" - that requires the source code!
...sort of. Source code access is important, sure, but here are a few more important issues that are basically orthogonal:
* The right to redistribute software
* The right to modify software (without source code?!?! Sure; imagine if I took Windows, removed the license protection code, and distributed that copy to you).
* The right to use software -- this, incredibly, can be a problem:
http://jalopnik.com/192843/robot-let-my-car-go-new-jersey-ga...
The purpose of the GPL is not to prevent people from modifying and building on the code. The purpose... well, let me quote from http://www.gnu.org/licenses/quick-guide-gplv3.html :
The GPL is a clever legal "hack" to achieve this, by allowing the code to be used only by others who agree to play by these rules. If the law were changed to enforce these rules directly, then no GPL would be needed. And eliminating intellectual property law restrictions on the use of code would get almost all the way there. (Companies would still be free to "protect" their code through secrecy: releasing only the compiled version and not the source code, but decompilers are pretty darn effective.)