I do not agree with your interpretation of copyright law. It does ban copies: there has to be information flow from the original to the copy for it to be a "copy." Spontaneous generation of the same content is often taken by the courts to be a sign that it's purely functional, derived from requirements by mathematical laws.
Patent law is different and doesn't rely on information flow in the same way.
Patent law is different and doesn't rely on information flow in the same way.