Imperfect phase alignment in ANC contaminates the wanted signal
Evidence
In the active case, the wanted signal is having noise added to it – not something one really wants to be doing if one can avoid it. If the phase shift is not absolutely correct, complete noise cancelation will not occur, with the result that the wanted signal is then being further contaminated. Furthermore, because of the phase shift requirement, higher frequencies are not attenuated as effectively—something the passive types do very well. — David Howard, Jamie Angus, coustics and Psychoacoustics, 2561