I can understand the reasons for this in a professional production, theatre, concert, ballet etc, but why should it be thus in a amateur situation? You have paid for the lessons, it's your children who are performing, the Studio wants customer satisfaction and will get some (free) publicity out of it from happy parents.
Maybe the Ballet School could be persuaded to see matters in a different light. (No pun intended

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The parents have charge over their children's rights, so if parents refuse to cooperate in the exploitation of their children for the financial gain of others without adequate recompense, the Professional, or the Dance Studio, would be unable to take photos. You then have a bargaining point, and that could be the ability to take your own photos during a set period, or from an agreed position, providing of course that there is no disruption to the concert. I know that Professionals have to make a living, but I cannot see that it should be to the detriment of the paying public to take photos of their children.
BTW, some excellent photos.