for one thing, it's almost certainly illegal to fly a drone in this circumstance. it's over a large crowd of people and could also be construed as "interfering with emergency services". knowing what can happen to people who are making legal recordings, I'd hate to be the odd one out who's actually recording illegally.
This answer baffles me. The illegality is moot in a political confrontation like this. And how are they going to know who's flying it? You do so from cover and give the footage to a journalist you trust. Your main problem is the risk of losing the drone.
most people at a protest (in the US) are not actually doing anything illegal. by attending you are certainly risking arrest and/or getting roughed up, but the police can't put any real charges on you unless they're willing to completely make them up. you're more likely to get harassed as a person with a smartphone camera, but the consequences could be a lot worse if you get caught operating the drone.
also, I think you are underestimating the odds of getting caught flying a drone in a city. an off-the-shelf consumer drone is probably only going to have about 15-20 minutes of fly time, but you need to give yourself a good buffer to fly to/from the location. if you just want to record a single ten minute video and call it a day, you'll probably get away with it. but if you want to record a meaningful amount of footage, you need to keep recovering the drone, swapping out batteries, and relaunching. this creates a lot of opportunities for someone to see you with the drone. if you crash the drone and the police recover it, there could be enough metadata on it to identify the operator.