Why doesn't negative reinforcement have the same problem?

Self-applied negative reinforcement has the same problem, for the most part: the fastest way to stop it is to just stop doing it.

The reason that negative reinforcement applied by others works (when it works), is because the fastest way to make it stop is to comply with the wishes of the one applying it.

Ideally, the act of compliance itself should make the disturbance stop, in the way that a properly used rein or choke chain on an animal should produce relief from the restraint as soon as the animal stops, turns, etc.

For a more human-relevant example, one can imagine a parent's frowning look as the child approaches a vase -- a frown that goes away the instant the tiny hand withdraws.

(Whether this specific example of training is actually a good idea is an entirely separate question from whether it's effective.)