But how would you "motivate" the formulas without knowing where they came from? Why is this the formula we use and not something else?

To go back to the car analogy, I know why I need an engine, you might even say I know how to use the engine, but if the engine dies or I want to use the engine for some other purpose, I'm not equipped to do anything.

I don't have "literacy" with engines, I have rote memorization of a series of steps. I don't have enough information to know why the steps are what they are, nor could I know under what conditions the steps should change or what they should change to.

Just don’t include formulas you can’t motivate simply.

Will it result in students not knowing as many formulas? Of course, but who cares?

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.

Which works pretty ok in medicine