I just did an impromptu shoot of a dance recital, actually 2 shows with just 2 days notice, just this past weekend.
The Director/Owner requested me to be her "official" photographer with a non-binding agreement. Meaning, I only provide what I can given the time constraints.
This all started because I volunteered as the photographer for the class photos that will be in the recital program and another of her school's event. I guess she liked how the photos turned out so she asked me to do the recital as well.
So it's good to be noticed by the owner beforehand so you have at least positioned yourself to be the "official" photographer.
Even now, we're already discussing future shoots of her other school events.
As to the no photo/video policy ...... I was working alongside the official videographer and we both agreed that we don't mind parents taking their own photos or videos but ... Those guests who just can't understand how it's potentially (and I mean potentially) dangerous strobes are for the dancers. It's quite disorienting especially if multiple strobes are firing at one time. The house staff had to approach these guests to remind them of that policy. House policy was "No Flash Photography". As for videos, I think it's more of just a matter of courtesy. Imagine lots of bright screens right in front of you while you're trying to enjoy the show. Kinda annoying, really.
Edit: Oh yeah, just to add more info. The school's Director did not and does not have any monetary interests on the photos that I took. If I ever sell any of the photos, all the profit are mine. The only thing she asked for was if she finds photos that she likes, that I give her full, unrestricted access to them, which sounds very fair to me.