I don't think a PG child would be actually harmed by a lack of acceleration, necessarily, but could be greatly frustrated and academic development in areas of interest delayed. Over-scheduling could represent a failure to address a child's academic need and ability to focus more usefully on something else. (ETA: I'm ashamed of the poor construction of that sentence. What I mean is that over-scheduling in an area not of interest to a highly self-motivated person can have bad effects, including curbing passion and stunting growth in major talent areas.) I think it would be worst if the extracurricular focus were chosen by the parent.
So I think it'd be failing one's PG child talented in math to make them attend a sport or dance activity for so many hours a week that they were effectively shorted in the math area, or didn't have enough time to develop their own interests in math-related subjects. PG children are often self-motivated to a large degree, and I think one should give full rein to that if possible. I think it's more likely that something like dance or an instrument will be initially chosen by the parent and will essentially be a chore that the child works at because the parent thinks it will be good for the child in the long run. The child may develop somewhat of a liking for such a thing, but unless the talent and inner drive for the subjec is present within the child at some point, it'll just be a form of hothousing that shorts academic development. But if the desire for heavy scheduling of a particular activity comes from genuine interest by the child, and the activity is healthy (gotta put the crack-'n'-video-game disclaimer in), it's not bad as long as enough balance is maintained.
With HG+ children that can learn at a faster pace, I could never agree that 1, 2, or any specific number of grade skips would be enough. That would just level-set 1, 2, or X times without addressing long-term the need for a change in pace and/or how the material is learned. A certain number of skips might work fine in a particular case, but not (clearly) in all cases. The likelihood that 1, 2, or any particular number of skips is plenty of acceleration goes down the further up the ability+drive scale you go.
Let's say I had a HG+ child with a math talent, who could learn 2-3 grades' worth of math concepts per year without stress, and also had an interest in math and STEM subjects (computer programming and robotics, say). Would I think it was a good move to insist that such a child spend all their free time on dance or a sport, or anything in specific that I chose? No. Now with my older son, he does have such interests, along with a range of other things he's interested in. Yesterday he decided to start building a model of the Eiffel tower out of toothpicks and Kix cereal nuggets (turns out they work better than marshmallows, performing much like tiny styrofoam balls). My belief is that he chooses things like this to do because he's interested, and also because some part of him recognizes that it needs practice at certain types of problem-solving, which I'd hate to deny. I also think that creativity needs free time to develop properly. Dance can certainly be creative, but hours per week of practicing plies, in order to hopefully perform an original work created by someone else, seems more like skills practice than (direct) creative talent development.
I'm just presenting a different point of view that I honestly hold, not arguing for the sake of argument. I don't think you're doing wrong by your daughter, though, because I don't know you or her, what prompted the specific choice of dance, or how much she's deeply interested in it. I also realize that if your daughter turns out to have world-class dance talent, including choreographic ability, she's going to need to develop basic skills in order to support her talent. And you are certainly providing valuable life experiences for your daughter, with trips etc., that a lot of people can't provide for their children. Parents all lie on a spectrum with their beliefs about things like how much to control their children, including how much to schedule their time, etc. I don't think anyone could say that a highly self-motivated PG child would be harmed by a mere two skips, either-- she would probably find some way to learn what she needed to know, even if that meant staying up at night reading and thinking.
And there are plenty of children out there that don't need or couldn't handle radical acceleration, of course-- sort of like the way one doesn't need to pour jet fuel into one's Ford Escort. Most of these children could probably get some value from a range of extracurricular activities, too. As has been discussed before in other threads, though, I don't see a lot of value in scheduling any child's time to the hilt, for many reasons. My feelings would change in a particular case if the interest came from the child, and the child was asking for a particular set of activities.
Somewhat off topic, but dance-related-- I saw "Black Swan" recently. Great movie!
