I really enjoy this post, @rsl12 .
As someone who's quite neurodivergent (auditory/visual synesthesia with music; play music completely by ear; figured out basic-intermediate music theory independently from formal training; pepped with some mild ADHD; born with harmonization since I was a toddler), you talk about improv in a way I hadn't thought of before.
For me, I was "born" to improvise so to speak, but completely bereft of ideas of discipline and structure. So I began my piano journey completely improvising, and without any polish at all, until several years ago. That is, I didn't even try to really play the piano seriously until I got our current pianos the last couple of years. Prior to that, I was simply playing highly undisciplined manner, that was great for showing off publicly, who think I'm some sort of "prodigy" since I could "play anything" on the spot. [I play more "wild" and "impressive" when I'm not recorded].
But really - I simply have the vocabulary of the notes/relativity/chords down pretty pat now, so it's second-nature. For me, it's very easy to play almost any "dumbed-down" version of any classical melody on the spot on any key, than it is to play the easiest classical melody correctly (i.e., tempo, voicing, etc., that's that are completely foreign to me).
Anyway, improvisation really isn't rocket science, or that esoteric. It can sound impressive, but it still boils down to lots of what you said.
This is mostly me just reflecting out loud. Thanks for de-mystifying what improvisation is, and articulating a gateway for those, who formerly were hesitant, to explore.
