They do, but not in the intuitive way one would think. They work because there's a passive seal around the hearing, thus the headphones only have to cancel the smaller amount of noise that gets into your ear, not the full loud noise outside in the environment. This is why ANC need to have mics inside your ears.

The problem is actually that the louder the noise, the louder the noise canceling would have to be. And at a certain point the passive seal cannot stop much of the outside noise, and if poorly designed, if the speaker tries to cancel that noise, it would be blasting massive soundwaves into your ears. But most consumer speakers can't achieve that and don't even try. So after a certain threshold, they won't work and can't help you with the noise. And the passive noise block is not even remotely good enough as a straight up earplug. So they are not considered protective gear, at least not the consumer devices, only aviation grade ANC is considered protective gear. But you'll see that they have massive ear cover,s with huge speakers and drivers, and elastic tensors on the headband to absolutely seal your ears and some truly state of the art audio processing that would make the most snob audiophile blush in envy.

They do make some of those for ground crews, construction sites and heavy machinery, but they insists that they are only effective if paired with a sound baffle earplug.

Noise cancelling earbuds or similar do not protect your hearing.

They do not make a loud noise quiet. It does not matter if they are working or not. All they do is make noise seem quiet, you are still being exposed to the same level of noise.