Say for the sake of argument that the US government decided to ban all encryption in communications. Since modern encryption makes a message practically indistinguishable from random noise, would sending random noise also be banned? If not, and since there's no practical way to tell them apart, how could this be enforced?
However, let's assume that this is true, for the sake of your question.
It depends on how the statute is written, but a reasonable one would not make it a crime to send random noise.
It could be enforced by proving that you did the encryption, and then sent what you encrypted across a communication channel. They could have undercover operatives waiting to be sent encrypted material. The encryption system that a user chooses to use might not be as secure as advertised (making it very easy to distinguish from noise if you know its weakness).
If all the government had was access to the communication channel and listened there, then you're right, it would be hard to prove and enforce, but they have access to more than that.