In the West we also have a tradition of nobility dancing too--IIRC for a while dance was one of the things young nobles had to learn. I was reminded of that while listening to the New Years' Strauss concert on youtube the other evening. It might be beneath the dignity of some sufficiently august ruler to try to cut the rug, but the tradition was still there.
How about in China? You can't imagine the Emperor on the dance floor--I'd think there'd be professionals doing the dancing. Turns out that different dynasties had different ideas about that. The dances were apparently often also important rituals--though sometimes peasant dances might be reworked for the court.
Persia had court dances too, for amusement and for ceremony. And later: "The harem of Nassereddin Shah, the 4th Qajar king, hosted dance performances in which many of his eighty-four wives and a number of his daughters participated. At the time, Shiite law forbade any kind of dance, but the most powerful man in the country had the luxury of breaking religious law."
I wonder what they were like.