Active noise cancellation devices that I've heard of try to analyze the noise to predict what it will do next so they know what to cancel out. They're expensive because they have to be fast enough to react to changes in the sound, and imperfect because they will always lag behind changes to the sound they're trying to cancel.

If you could identify the song then you could simply fast-forward it to know "what it will do next" and the cancellation would be much easier and more accurate.

This kind of noise cancellation really only works on constant drones, not more complex waveforms like music.