Some excellent point raised, Resonox. I think it's fair to take into consideration that your average Joe (or Josephine, before anyone says owt) doesn't even consider that their actions could possibly cause any damage.
Of course - as has been discussed many times - it's unlikely one person WILL cause any damage, but multiply that by a million (number plucked from the ether) people all with the same thought, and erosion/damage is bound to occur. And one person giving themselves permission to do so then has to accept that ANYONE can give themselves permission to do so, and therein lays the issue.
And this is why the code of conduct would be such a great idea. At least then people will know WHY they shouldn't be climbing the monuments, and if they persist, then hopefully others who are aware of the code would intervene. At the very least, there'd be no excuses for those who consider photo opportunities of people jumping around on them is a good thing.