I hate white noise and It bugs me a lot in current office settings (theory is that my brain is trying to make sense of what's thrown at it). Isn't anti-noise signal, in itself, a noise? Whether or not it perfectly matches the noise signal or lags behind. Wouldn't that be more patterns that the brain would try to make sense of.
https://en.m.wikipedia.org/wiki/Wave_interference
The goal of noise canceling is to fully use destructive wave interference to create a 0 amplitude "signal", which is no signal at all.