The generalization of this point is "what's the case for live anything" which can be answered simply with "presence" or more broadly, shared experience.

Sport is only the most obvious example. Why doesn't everyone just record and watch the game at their leisure? Or just get the highlights? Sure, those are options, but the enduring appeal of live sport points to there being more to it than just consumption of information.

But the generalization of the point removes the point I was referring to. I'm not going to argue that live sports are popular for a reason, just that live watching a large number of people attending protests is less so.

I suspect the original commenter was just using a topical example, but ok, let's say it's protests.

A very large number of people streaming might create a curation requirement, but that's all. You have someone reputable who is retweeting or directing people to the most useful feed (as happens already with breaking news events on Twitter).

You end up watching someone having a dialog with a police officer, or in the middle of a rush, or something. You feel a greater sense of connection knowing that it is happening right now.

it doesn't have to be protests.

Periscope for ESPN and watch the hosts betweeen quarters of some football game.

Periscope for famous people and watch them go on stage or whatever.

Periscope for you and let your family and friends meet your newborn asap.

Periscope for ESPN would be interesting. do the leageues allow that since you are essentially broadcasting the match/event?

The live part would be really useful if the police decide to confiscate your phone before you have a chance to edit and upload anything.

The people streaming have no time for editing. Moreover, video editing is unnecessarily painful, so amateurs hardly ever do it. What does happen is the best stuff gets saved and recycled as GIFs/HTML5 short videos.