If a line was visible at the entrance I think we would discover that there are far more stupid than we realize. It probably would become a beacon for those "stupid", and seen as an invitation to follow the line in, believing that the line alone would provide safety to divers who are simply not aware of where the true risks lie.
I might be inclined to allow natural selection and heard thinning to take place if it weren't for the fact that it would bring unwanted attention to we cave divers.