I think this is a key point. In my favorite writing course in college, the professor chose to teach composition from the perspective of legal argumentation. We wrote 4-8 pages per week in the most economical and intentional way possible, poring over every word, every sentence, and every paragraph to make the language easy to understand and to make every word do work.
The professor never pretended that this was the best way to write and never claimed the result would be beautiful, though he did claim that the result would be easy to understand, which it was. Peer editing in that class was the smoothest experience I've ever had in a writing class. But he accomplished something that no other writing instructor did for me before this class: he taught how to make grammar, diction, rhythm, and even connotation an intentional thought process. He also taught how to think clearly about the point you wanted to get across.
That wasn't going to teach any of us beautiful prose or how to craft good plots, but it got us very quickly to the point where our writing style became deliberate.
(I have made this longer than usual because I have not had time to make it shorter.)
I've learned to explain in terms almost stupidly simple because another's interpretation can be so extraordinarily far from your intent you wonder how they even got there. Then they explain how it reads to them, and inside you groan a little because yes, it could be seen to mean that and you had no idea. One needs to user test one's writings just as much as one's software, I've discovered.
[0] WIP
I would argue precisely the opposite.
You can't build beautiful woodworking until you can do a joint reliably and repeatedly. You can't play jazz on your musical instrument until you can play scales reliably and repeatedly.
You had a really excellent writing professor. He completely anchored the fundamentals that you needed. Now you can actually proceed to actually write.
Not going to speak for my own writing, but I completely agree with your point. The better you understand the fundamentals of composition, the better you understand what makes good writing good, how to hone your own style, and how to tailor your writing to the situation.
I think of The Elements of Style as one of those attempts to break writing (in English) down into its mechanical elements. Whether or not I agree with its advice, I respect the approach it tries to take.