See the comments on the main “access” page of the wiki about theory versus practice. I believe that of the 3 routers on the main osm.org page, OSRM will route cars and bicycles on such a way, GraphHopper will route bicycles but not cars, and Valhalla will only route pedestrians.
But also, this tagging (without additional tags like motor_vehicle) seems to be rather rare. As suggested in the previous post, your examples may be useful if they suggest systematic patterns, but less so if they are simply occasional misunderstandings.