How the Taliban take over a village is similar to how a gang takes over a neighborhood.
Indeed, and they can get away with it through carefully applied intimidation, "night letters", and outright murder during visits in the night.

Are we unable to stop them simply because we often do not have a durable presence in those villages, like a beat cop should have durable presence in his assigned neighborhood? Or is it more due to a lack of a mechanism for said villagers to anonymously report when the insurgents are maneuvering through their land/homes?

Put another way, does law enforcement succeed primarily from presence or speed in response?