Sometimes they'll need formulas they don't understand (can't motivate) for doing work things?
Then what? Are they going to incorrectly use anther one, a wrong one, because they understand it better?
(Searching not where one lost the key, but where the light is stronger)
Hmm, I wonder if you studied stats? It sounds as if you studied lots of math.
I did long ago, mostly forgotten, and, hmm, I don't think there's a single real life useful probability function one can understand, without knowing the underlying calculus? Except for understanding in the sense of trusting the teacher.
Will it result in students not knowing as many formulas? Of course, but who cares?