Yes. This is why it's always nice to keep a budget after the software is released.
Morover for version 1.0.
To listen, observe and discover the pain points, the surprising routes users make using the software...
Then you change the code to stock to the user behavior.
This is one of the two reasons why I follow a "ignore all software until at least version 3" rule of thumb. The other is to allow time for the software's major bugs to be found and ironed out.
Taken too far this can cause problems. Many have experienced the over-walked nature park where one can't even tell what the official trail is anymore. I have volunteered in public parks, and one of the difficulties is encouraging the use of the official paths, and discouraging use of the 'social paths' (as we called them), while maintaining the natural look of the trail.
As rascul said there are environmental concerns. There can also be access/ADA issues, like path width or slope/rise:run. Or it may simply be budgetary.
Low stakes with string or wire strung among'em should be enough in most cases to deter off-path tromping eh ? Plant something inside their perimeter so it all looks preplanned.
It's generally desired to put up as few artificial features as possible to maintain the natural look of the park. Sometimes it is necessary, of course.
The other problem is that many trails are just maintained by a couple of volunteers. Many in the US are done by local mountain biking clubs, for example. It can be hard enough to maintain what is already there when you're relying on the goodwill of a couple volunteers to do heavy labor at 6am on a Sunday.
That 20% there is the little fact that all the fences and signs in the world don't keep a certain subset of headstrong people from e.g. leaving the path and falling into geysers in Yellowstone, or getting too close to wildlife.
It's not that they're more popular. It's that the entire forest becomes one big social path devoid of ground cover flora. One purpose of paths is to keep human disturbance to a small, well-defined area.
If they were obviously more popular, that's what we would do. But usually it is all just a big mess of erosion and there isn't any obviously most-popular path.
You are describing a case where the desire paths are undesirable, as they may allow litter or vegetation growth, or hasten erosion of soil.
However, when you mention "even tell what the official trail is" is a desire path still desirable in this case? I mean, if no one knows there is an official trail what purpose does the desire path serve? Or is your concern about having interesting vegetation or whatever spoiled by the desire path?
I wonder if there is an optimum amount of desire paths -- where it is still possible to follow the official trail, but interesting diversions are also allowed.
I remember thinking about this phenomena in arch school musing over the paths taken. It's interesting that OP calls this "desire paths". My thoughts were that these are more akin to orbits, or how rivulets establish a path over dirt, i.e. removed from notions of desiring.
But I like the desire semantics. Supressing desire can build excitement. In fact, a very typical architectural device in ceremonial designs is to either slowly reveal, or to reveal and then take you on a long path as you slowly and finally reach a space or object. Architecture is, possibly, all about controlling desire. So collorary to the desire path is 'desire denied/delayed path', equally important to have in a designer's toolkit.
Then you change the code to stock to the user behavior.