My knowledge of ANR may be a little out of date but here goes. ANR within a headset works very well and can cope with a range of frequencies. The RAE (as was) extensively tested ANR systems in a wide variety of aircraft eg Harrier, Chinook, Hercules etc. It was very good at reducing noise levels at the ear and used an analogue system. It certainly cancelled across a range of frequencies, maybe 100Hz to about 1kHZ, but I can't remember the specifics. I now use a Sennheiser ANR headset and subjectively it works very well especially at reducing boundary layer airflow noise at low level. The rules have changed now but until recently when ATC said "no speed restriction" the aircraft would wind up to about 340 kts and at 6000 feet it got pretty noisy!
I know that during the 80s and 90s there were companies researching a cabin system using an array of mics and speakers. As someone mentioned there was a design incorporating the speaker/mic combination into the headrest. Certainly, SAAB and Lotus cars were involved but I don't know how they fared.
I think it's probably correct to say that wide area ANR systems are not easy to build but not impossible to do so. What very likely does make a big difference is what type of noise you are trying to cancel and whether you are interested in cancelling noise at very specific locations eg pilot/pax head location as opposed to over a wider area. Some pretty hefty digital signal processing is required but computing power today should not be a problem. Another factor is whether the noise is broad band eg airflow generated or discrete such as prop/rotor noise (or even as in the case as helicopters from the gear box/transmission). It won't come as a surprise that a narrowband discrete source that can be tracked in some way is much easier to cancel. Also, the prop noise by having a longer wavelength is easier to cancel than a short wavelength (high frequency).