They have a thing called a stingray which can impersonate a real cell tower for the purpose of gaining information about the phones in range. That would be a very effective way to create a list of phones to temporarily disable.
That would not be very effective for the kind of cover up you were speculating about (disabling phones so they can shoot protestors without it being widely recorded on video).
First, they'd have to set up a Stingray. Then they'd have to get the phone numbers. Then for each number, they have to go to the appropriate company and ask that company to do the kill. Note this only works for smartphones. Feature phones are not required to support a kill switch. There are feature phones that include still and video cameras.
That's going to take a while...and it is going to miss a lot of people in addition to those using feature phones. It will also miss tablets, laptops, and GoPro cameras.
If, improbably, the only people with cameras in the protest are people on smartphones, they still have almost no chance of making the coverup work. To get the kill switch applied without court approval, they have to claim it was an emergency, and then justify retroactively that shutting down phone communication was necessary because of that emergency.
They will not be able to do this, since it is almost impossible to come up with a legitimate emergency situation where using the slow and incomplete kill switch mechanism is better than simply shutting down the cell towers that serve the area. Going for the kill switch instead of shutting down the towers is practically admitting that they were not actually trying to stop communication (which could conceivably be a legitimate response to some kinds of emergency) but rather were trying to stop cameras (which almost never can be a legitimate response to the kind of emergency that can arise at a protest).
1. Setting up a stingray takes very little time if it's already mounted on a truck or a trailer.
2. Phones and towers are constantly looking for one another so that phones are always connected. This is how you are able to talk while driving or moving. You might get all the phones in an area in a few seconds or minutes.
3. You make a good point about the per-phone nature of the thing. How long before law enforcement has a kill-a-phone API though? Facebook has a dedicated website for law enforcement to get info on Facebook users.
4. Your point about missing other devices is also a good one. But again the police can arrest people and prevent the information from getting out.
5. I think your statement about simply shutting down the towers is the best counter-argument. You're right, they can just kill the towers, even without phone company assistance. Send a few officers with bolt cutters and towers will go dark.
6. There are all kinds of after-the-fact justifications for doing something especially if you're in control of the situation. You can claim basically whatever you want. Law enforcement is generally considered more reliable by the courts than regular people; cops say X and protesters say Y and judges are likely to believe the police. This is well documented.
The cynic in me says that #5 will never happen because it involves hurting big business. You can shoot up poor people with impunity, but you can't go around destroying property belonging to large companies without serious repercussions.