It doesn’t have to be perfect to still be effective. Let’s say you have a sound coming in at 150 dB, which is definitely not hearing safe, and the headphones have a delay so they can’t perfectly match up the anti-wave directly over the incoming wave - as long as the anti-wave moves the crests and troughs in the right direction, you create this new wave that’s mostly cancelled out, but you might get some, like 5 or 8 or 3 dB through, which is much safer