Chesterton finds himself surrounded by fences which have no articulated justification, but which might be necessary/justifiable. This is a predicament of his own making. If he and everyone else in the town always bulldozed any fence they came across which doesn’t have a justification, people who want fences would start writing down why they’d put them there.
This would be helpful, because not only will it tell us which fences shouldn’t be torn down. It would tell us which fences we should actively maintain.