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.
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.
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.
If the official trail is too wet to walk on, it's too wet to hike that day.