If someone shoots video of a parade and captures the people in the background that's different. They were intending to capture the parade and were hopefully focused on the parade. If someone is standing on the parade route shooting only the people in the crowd and happens to get some of the parade in the shots, that's different.
When a person straps a video camera to their head and walks around the park recording, or sits on a bench recording, they are not intending to shoot a parade or take pics of their family.
If a child was in waiting for the parade, twirling in her new princess dress and her underwear was exposed, how would you feel if you saw someone whip out their camera and take a picture of her. (But what if she exposed her undies when the parade was going on? So what you're saying is it's okay to videotape a parade until a child accidentally exposes her underwear? Do they now have to erase the recording?) Now imagine that someone with a Go Pro on their head looks at that girl for 2 seconds and captures 100+ images of that scene. Think of how many times you've seen someone whose shorts were too short or too low on their waist in the park. Would you think it's appropriate to take photos or video of that? (Yes, if that person decided their attire were suitable for public. Or even if they were clueless how inappropriate they looked.) Anyone with a Go Pro on their head or concealed in their hand can easily do just that, intentional or not. There are thinks that I think we can all agree would not be appropriate to do with a camcorder or point and shoot camera that are not excused just because they now sell cameras that you can strap to your head and shoot continuous video and then easily break that down into individual frames.