I'm in my 20s and I've been going to ballet since early 20s. Personally I hate seeing a phone screen lighting up during the performance, it is very distracting for me, not just in theaters but also in cinemas.
But I don't think that capturing moments in pictures and posting it on social media in general are vain and unnecessary behaviors, nor I associate it with disrespect for the dancers and the orchestra. Personally I would not do it because I'm usually way too busy concentrating on every element on the stage. But I can't tell other people how they should enjoy the performance and maybe people might want to record the piece they already know so well.
That being said, I'd have nothing against anyone taking pictures IF they could manage it without capturing my attention with screen light, and if there were no explicit reasons for the theaters to forbid it like copy rights issues. Then there would be no reason for me to care.
Actually my best friend was a ballet dancer and she once took videos secretly when we were at the very back without people around us. Interestingly from what I've seen, dancers mostly seem to be less obsessed with etiquette as much as what the general audience thinks.
I do agree pictures and videos can have positive effects. As you said, it can indeed potentially help increasing visibility. Many people don't even know what ballet is like and often have a very limited and unreal imagination of what it looks like. Seeing the videos shared by their friends on social media can indeed turn a few heads.
Another positive side of it is that it helps remembering the details of the performance. I used to believe being in the moment without taking pictures was better no matter what I was doing. But I've realized my memory isn't as strong and vivid as pictures and videos after all. Even if it's just a small part of the performance, it would work as an anchor point to activate the forgotten details in memory. I often look at the pictures I took during the curtain calls. Seeing the stage set and the costume already brings me back to that moment and makes me recall further details of the performance.
So I partly understand the motivations of the people who want to take pictures of or record the performance. The only reason why I'd mind it is the distraction part.
