All kidding aside, this is some bullshit.
It's not that dancing is illegal, it's more about disturbing the peace. You can't go into a local restaurant where I'm eating dinner and start dancing or singing. Along the same lines, if I was drop thousands of dollars in plane fare and hotels to go to visit monuments in Washington DC only to have my afternoon ruined by stupid kids making a scene, I'd be pretty pissed to.
And these dumb kids will understand this more twenty years from now when they have kids of their own, they shell out a ton of money to spend a day at a museum or monument on vacation, only to have their day ruined by a bunch of stupid kids. I remember once at the Grand Canyon a group of four or five teens all bought ice creams cones, and decided to have a ice cream fight in the middle of the path. It was a five minute scene, and then I had to try to explain to my kid what was happening. I'm pretty easy going (and I've acted like an asshole more than once in Vegas myself), but there's a time and a place for that.