I think I remember reading of a mod ages ago which took away the markers on your in game compass for things like caves so you had to actually discover them rather than the game showing them to you on a plate. Is there such a mod and has anyone used it?
My http://www.gamesas.com/index.php?/topic/1141697-relz-map-marker-overhaul/ mod has settings that let you choose the distances from where the markers become visible in the compass, with default settings quite much closer than in vanilla, for the reason you state.
And yes, lots of people are using Map Marker Overhaul