They would like to have the photo in addition to the experience, typically so that they can remember it. Sure, you can look at a professional photograph of Times Square, but it's probably not going to help you remember the time when you were there. And you can't point to it and later and say, "hey grandkids, try to imagine me standing here but really young!"
It's bizarre to me that you don't understand this.
It's also strange that you think spending time taking a photo would cause you to somehow "miss" the experience - which, I guess would be true if the experience were a one-time only event that lasted a few seconds - but spending five minutes snapping a few photos at a two hour concert is not going to "ruin" anything.