There is already a visitors' charter
What is needed is for the gardians to accept responsibility. If 50% of the public take note of the visitors' charter it probably wouldn't stop stunts like the ones we've seen lately.
If the gardians sign up to it (and I'd add a clause about placing signs at car parks, too, asking people to take care*) then that's protection from most things, not just responsible visitors.
People likely to take note of the visitors' charter are not likely to damage a site anyway. Some folk you'll never get through to, so there's no point in a visitors' charter for them. Remember, even some of the folks who claim to hold these sites sacred often litter them**! ( from last week)
*Get EH or the gov't to pay for these :-)
** I did say some before anyone says anything.