I never said it was the most intuitive, just the most streamlined and most efficient. I'm having a hard time understanding why you think it's not the best organized. Most math courses are taught with a pretty straight forward approach: start with the axioms and definitions, prove the easy and auxiliary theorems that are easily derived from the axioms, prove the fundamental theorems that make the subject useful. In other words, the shortest path from the axioms to the important theorems. I don't see a way to make it more organized or compact, but I'm open to hear what you think is a more condensed or organized way to teach math.

And no, this is rarely the most intuitive or contextual way to learn math. Another analogy - a library doesn't sort their books by which ones were best reads or most influential, but by topic and author. Similarly, math curriculums are organized by a hierarchy of which theorems can prove the next theorem with no explanation of which ones are important. Organization doesn't always provide intuition.