What are the most common attacks? Punches - left and right straights, left and right elliptical/round. Possibly starting with a push. Most often very committed. Possibly followed by a grab/bear hug.
This is not to say that the other attacks don't happen, but I'd certainly rather spend most of my time, in the lower belts, training for the most likely scenario (The new student will thank me for it later). The more reps you have dealing with punches the more likely you are to survive a fight. Your white belt, who after one month of training, utilized the technique is the exception to the rule. There always will be.
The techniques really are not just drills. You can't repeat a technique as fast as you can a drill. Drills are for "Drilling" in a specific pattern of movement using very repetitive movements. Techniques are much more complicated and usually involve very different mechanics from one technique to the next.
True, you do have to pick out what works best for you. If you're happy, I'm happy.