I imagine a naive solution would be to add a gate to only cancel noises over a certain db threshold. Also you'd apply some digital signal processing to smooth incoming signal, something like a rolling average or low pass filter to avoid sudden spikes

In my experience the best case for noise cancellation is when there's a constant low level hum eg traffic or airplanes. It works wonders then. I was hesitant about getting a pair but they have been great for me (Sony WF-1000XM4)