I expected a website offering to use your microphone to record, invert and cancel background noise via the speakers. Turns out the website is offering prerecorded sounds instead, not really cancelling anything. Still though, surely someone has tried my idea? It would likely need some adjustability to match the phase delay between microphone and ears-via-speakers but I guess it could work.
Well, AFAIK some cars have active noise cancelation. I wonder why we don't have it at homes, after all they are both confined spaces. If general purpose computation and software wouldn't cut it, why we don't have whatever they have in those cars? A lot of money is spent on noise insulation on buildings, so the demand and the money must be there.