Certainly, if you are of the opinion, that openstreetmap data should only contain reproducible information on facts about what is on earth, these routes have no place in OSM.
Nevertheless, such stuff is in the data, the very case is exactly about that. So my question in other words: Is highway=path a proper and accepted method to map stuff, that has no On The Ground Truth to it?
I did not yet look at where the poll stands, from remembering last time and from reading along here, this seems widely held fine. Link to poll.
PS: In a recent topic in the Austria category on a similar concern, all but one commentor agreed: It is the trampling that makes the path, not the ideas of people creating a route.