Apart from speed of response that many comments mention, isn't there a more fundamental issue with active suppression using wave interference in a 3D space. There will be places where the superposition of the amplitudes of the original wave and the active/added wave will cancel each other out but there will be places where they will superpose additively. Hypothetically one could position the source of the active suppressing waveform where the suppression target originates, but that would not be practical. Of course, with smart and speedy enough tech one could arrange the waves to cancel at a specific point.
Even if you could track the head of listener and send a counter wave to the particular position it would be limited to a very low frequency sounds with wavelength larger than distance between your two ears. Also neighbors wouldn't be happy hearing two times louder noise as it would be without cancellation.
