An interesting article by a dancing psychologist. The self consciousness he talks about is very understandable. This is just more obvious with dance, since it is a social setting, but having people see how uncoordinated we are is uncomfortable to consider. How many people would abandon playing tennis, or even jogging, if they knew they had an audience?
There are relatively simple ways to improve how you move, without surgery. Perhaps we can't all be as graceful as Fonteyne or Barishnikov, but through regular dancing we can all become more graceful than before we started dancing. Training is good, but even just doing it, getting your body used to moving rythmically, finding joy in movement, will improve your physical grace. And isn't that what we most enjoy seeing in a graceful adult, or in a child--their apparent joy in movement.