That is a great question and no, mixing in noise makes it harder but doesn't make it impossible. Mixing in noise feels like a solution because it is hard for a

That is a great question and no, mixing in noise makes it harder but doesn't make it impossible. Mixing in noise feels like a solution because it is hard for a layperson to see how a signal can be extracted, proof by "difficulty to me". If you mix in noise that changes averages then you are removing signal. If you add in random noise, each individual measurement deviates, but the limit of the average will be the same value pre-mixing.