Very simply... Safety and Consideration.
As anyone who has attended a stage performance before will tell you, before the show begins, the "house" lights go down. This creates a situation where performers on stage are looking out into a darkened audience and their eyes tend to adjust to the low levels of light out in the audience.
Because of the nature of stage lighting, performers cannot see much further than the end of the stage. It’s likely that they might not even know that you are out there ready to snap their picture. When a flash on a camera goes off and a performer happens to be looking directly at it, they can, and do; sometime get temporally blinded seriously compromising their ability to see on stage.
Spotlight allows flash photography during dress rehearsals only. This because, unlike performances, house lights are up and performer’s eyes are fully adjusted to the brighter light beyond the lip of the stage thus mitigating any danger. In other words... not performance conditions.
With today's high resolution video cameras in everyone's phone the reality is fewer and fewer people feel the need to purchase a professionally taped video. So, Spotlight policy is to allow people to video at will during performances. We simply ask that you follow two rules.
1) Be considerate of other audience members when videotaping. Please do not hold your device so high as to prevent other audience members from being able to see the show.
2) At no time is taping from the front of the house allowed. If anyone moves to the front of the house, the show will be stopped until such time as the front has been cleared.