Funny you asked, Freaky...
We used the threaten to take away the dance. But over time we realized (and this was much harder for Mr. Balletmom to get) that taking away the dance for anything less than a major transgression (and maybe not then) was counter-productive. We used to threaten it for grades, but we had enough issues with one teacher to realize this year that we might be punishing our child for one teacher's flakiness.
Also, the downsides of taking away a performance--as you said--seem to outweigh anything productive. She would be forever marked in the director's eye as unreliable. Plus, knowing the "backstage" side of it so well, we would know very well what difficulties we were causing everyone else.
We did keep her home from one class this past semester, we were trying to figure out the latest email from Flaky Teacher--a combination of a late paper from Flaky Kid and Flaky Teacher's unique averaging system.
But overall, we don't keep her from dance, and we don't let her stay home from school to recover from dance, either.
Also, now that she's on pointe, she can't really take time off. Two weeks is the limit as far as not stretching/dancing. If she stayed out a month--it would just be the end of her dancing, or a very difficult recovery. So it's not really something we would do at this point unless it was a really serious transgression.
And finally, I think the structure of dance is itself more productive. It's physically exhausting and keeps her out of more trouble. I've seen some horror stories of kids who were cut from high school sports and then just fell apart, so again--it wouldn't accomplish anything good and would hurt more.
It seems to work better to just go in and take her computer keyboard, or her i-pod. (She's lost her cell phone!
Probably somewhere in her room.) The keyboard is much more her "recreational" time since she loves doing graphics. Especially when we say, "We'll just let your teachers know that they need to give you an alternate assignment since you are grounded from the computer."
I'm actually horrified your mother threatened to take away your music if you didn't lose weight. I certainly am not up for parent of the year (if you had seen us throwing a fit in the Ikea parking lot when the older one acted up with the younger one's i-pod you would have certainly called Dr. Phil for an intervention) but I can't believe your mother would take away something you loved and were good at, to "encourage" you in something like losing weight!
I have come to realize that my daughters both have an "identity" in being dancers. It's important to them, they are good at it, and overall, they make good grades. ( The assistant principal said when we getting into Flaky Teacher, "Oh, Balletkid? I know her. She's a good kid.") So while we might have once said "The dance goes at the drop of a hat!" we are much more careful now, because there's a whole lot of bad stuff waiting out there to suck in a kiddo without an identity.