That is the same thing I always try to do. I opened a closet during the White House tour... got in some trouble for that! In other countries, though, I feel like they make their landmarks more accessible. Chichen Itza is not just a national monument, but a religious one, and you can climb all over that place. No guards, no supervision, complete unrestricted access. If we did that in the US, there would be graffiti everywhere.
If you did that in the US Ozzy Osbourne would piss all over it!!