Open Source software can exist in a world without copyright; that's basically what permissive licenses are. Proprietary software can exist in a world without copyright; just don't release the source code, only distribute build artifacts. But free software is dead without copyright.
Most permissive licenses — and most popular permissive licenses — include a copyright statement and conditions which would not be enforceable without copyright. They usually require redistribution of the original copyright notice and license text to be distributed along with copies or derivatives of the work.
That doesn't mean there can't be other legal mechanisms that would also accomplish software freedom.
Closed-source software should just be illegal. Then you don't need copyright to ensure freedom. With copyright gone, you are now guaranteed free to reuse any code. The law should not prohibit copying, it should only require attribution (i.e., prohibit plagiarism).