As someone who has spent a great deal of time on stage, I can tell it you that it can be massively distracting. But in my experience, it's usually not the performer's request, but the agents (if there are any involved) who don't want anyone else to have quality pics of their cash cows. I think the majority of restrictions fall in this category. I've noticed that in a lot of museums the lighting is so poor that it's damn near impossible to get good shots. The only reason I can think of is that they want to sell you a postcard. TBH, I don't want their 50p postcards. I'd rather pay a £10 admission and be free to take my own pics.
The other issue is with venues where they don't necessarily have flashing lights. It just looks bad if someone has an epileptic fit and dies in your club. Depending on where in the world you are, that might come with some liability, although I think that's silly.