A conventional explanation of desire lines, as found on the all-knowing ever-changing hive-mind of Wikipedia, runs something like this:
Desire lines emerge where the shortest route between a point of origin and a destination has not been officially marked and yet is walked anyway.
With increasing use, the path becomes permanently visible, its width and the depth of erosion, indicating its level of use.
But this limited definition is born of the need to define something born of a need to defy definition.
Desire lines do not always leave a trace. On grass and on soft organic surfaces paths may be made obvious over time. But if countless walking feet do not leave an impression, this does not negate a collective desire to walk that route. Desire lines also exist across city squares and hard surfacing where they leave no visible trace.
Surely, once a desire line becomes visible in some way, it becomes just another socially accepted path. Its value as an indicator of individual desire diminishes.
And what about the desire lines that no one else ever sees or feels? Desire lines may exist in no more than a single mind. Just because it a desire is not universal does not mean it does not exist.
Desire lines are, in the first instance, a symbol of individual thinking. The moment they become well worn, they lose that pioneering state. If someone else follows a previously trodden path, are they following it because that is what they, in their heart-of-hearts desire, or because it has been sanctioned by previous use?