Hmm, if it's just rules/fines, the chances are 0% that no one touches the thing, because it seems like guaranteed that an idiot will one day walk in there and touch something they're not meant to touch.

So if you want to preserve it, probably barriers/distance is the only good enough protection.

Putting any of this on display, barriers or no, means you're slowly destroying it. If preservation were the primary aim, nobody would be allowed inside except epigraphers and photographers. Want to see these monuments? Look at the photographs, drawings, and models like this.

They have, but a lot of people can't be arsed.