Coming from an ex MSF instructor. In emergency breaking you always should be taught to pull the clutch in and keep down shifting until you get into first. As others have noted it is so that you are still in control of the bike ( even though you are in emergency breaking mode ) and if the circumstances change you are still in a position to get out of the emergency breaking and go into evasion mode.
A lot of what is taught may seem odd, but what they are trying to teach you is basic muscle memory so that you do the same thing over and over. In an emergency situation you will always revert back to what you were taught.
Another good example. Is that every time you come up to a stop and the bike is upright and straight, always use both brakes. It is a valuable exercise to practice this in a safe location. Gradually apply more and more brakes ( keep your speed down, no more than second gear when doing this). You need to learn how the bike handles under different types of braking and if you have ABS how it works. If you are one of these that only uses either the front or rear brake all the time, when you are faced with an emergency situation you will still only use the one brake or you'll clamp on both brakes too hard and loose control of the bike. On a MSF course I've seem riders apply too much front brake and go right over the handlebars.
To be a competent rider you always have to practice your skills so that they are going to be there when you need them.
1971 R50/5 Cafe Project
2013 DL650 Adv