It is fast, often faster than most people can pull the trigger. It can really help to fire two or three rounds in the same sight picture, especially when you know what you are doing and can keep them tight.
Armed confrontations seem to be, for the most part, quick and violent. Most are over in a matter of seconds, with the really long ones typically not lasting for more than an hour.
During this time, everyone is moving, and everyones goal is to kill the enemy. People have kept fighting after taking a 5.56 round to the chest. Not many keep fighting after taking three.
The military went to three round burst after Vietnam largely because guys were using M-16s like bullet hoses, ripping off mag after mag and, frequently, not hitting anything. This led to troops on the ground with no ammo, and the logistical problems that follow. With a three round burst you have to pull the trigger 10 times to empty a magazine, and there is no illusion that you must have hit something with all of that fire.