A dancing chair would be awesome, and if done right, you wouldn't have to worry about certain chairs, er, not being able to handle the strain, lets say!
That would be one of the biggest things for me- a chair that can handle people being rough with them. I know one of the burlesque dancers in Vancouver, Lola Frost, does a lot of chair dancing...and she's rough! You can look her up if you like. At the end of one of her routines I had opportunity to see in person, she throws the chair down on the ground, after roughing it up for the whole dance! It was awesome, but...the chair had to be tough!
Otherwise, it's difficult to say, because so many people like doing different things. Lets say someone wanted to do an elbow stand off a chair...well, how would you be able to make it the right height? Even if the height is adjustable, you'd still have that strength issue.
Not to mention, if you're throwing your chair about (even by accident) you'd still want it to look good, without any paint chips or unhappy scratches!
Err, I didn't think I'd go quite in depth with this one 😉 Just things to think about, really! I would be quite interested in a chair to dance with, though!