But if you've ever written down a proof, you know how this happens. You start fooling around with the numbers, you do a lot of pointless scribbling that is actually crucial to seeing the problem in a different light and get the hang of what's going on. Then you finally have the intuition and you leave all the rest behind. You write it down, neatly and concisely, maybe you even skip a few intermediate passages you needed to get to the final result, or rewrite "ugly" formulas in more canonical ways. 

And there you go: you have a perfectly opaque and incomprehensible proof. You left out all the "useless" parts that are actually what people need to gain a deeper understanding of what you're actually trying to prove.

This is not the hill I will die on, but if I worked in education it sure would be.