I though I had replied to this or similar thread but can't find the post in my history... Anyways:

Proper active noise cancelling is hard and the algorithms patented to hell and back (since you actually do not get it to work by just recording audio and hoping to reverse the phase in actual realtime [not gonna happen]).

The good headsets with noise cancellation use multiple microphones in the headset itself since they need to get the noise your ears hear to be able to do anything about it (and they're not doing it by full phase reversal in less than nanosecond*), fighting the specific noise that goes to your pants-pocket is going to only add to the noise your ears hear.

So yes; it sounds like a great idea and "easy to do", until you start really thinking how to do it (or throw together a quick program and than start wondering why the performance is worse than abysmal)

*even if you have the mics at known distance from the speakers (so you know exactly how much the reversed noise needs to be delayed if we happen to be able to do the reverse faster than sound travels the distance) and the mics are few mm out of the speakers (which gives you more than zero time to do the reverse, not a lot more: 5mm gives about a nanosecond of time...)