When I was in the TA, in an IS (Internal Security) battalion, we were instructed never to fire warning shots or shoot over people’s heads. Warnings might be given, three being a traditional British Army number, but if fire was opened it was only ever intended to kill.
Doctrine was different in other armies, and is I understand now different in the British Army, but the reasons given at the time still seem good to me. In a civil disorder situation, it is important to control the level of violence. One critical transition in the level of violence is the use of lethal force. If soldiers are allowed to fire warning shots, then it is hard to be sure whether lethal force is or is not being used. If, on the other hand, they are prohibited from firing warning shots, confusion is impossible, and everybody knows, once they hear shots, that it’s no more Mr. Nice Guy and lethal force is being used. What you really don’t want to happen is someone firing a warning shot in a confused situation, someone else thinking they are being shot at, and lethal fire being opened without orders.
All the best,