Noise cancelling headphones work much better and are much easier to do than room level noise-cancellation. Why? Well, the whole point of noise-cancellation is

Noise cancelling headphones work much better and are much easier to do than room level noise-cancellation. Why? Well, the whole point of noise-cancellation is to create an interference pattern in your ear, that is as similar as possible to the noise in your ear. The farther you get from your ear that becomes harder, because of the room's acoustics, because of latency, because of the fact your head is moving, etc. And we see that in the results of room level noise cancellation attempts in the past.