He doesn't have to give proofs. Just explaining the intuition behind each formula doesn't take that long and will help the students understand how and when to use them. Giving intuitions really isn't esoteric trivia for advanced students, it's something that will make solving problems easier for everyone relative to if they just memorized each individual case where each formula applies.
I suspect this is typical mind fallacy at work. There are many students who either can't, or don't want to, learn mathematical intuitions or explanations. They prefer to learn a few formulas and rules by rote, the same way they do in every other class.
Another month has passed and here is a new rationality quotes thread. The usual rules are:
And one new rule: