There is no such thing as genuine "intuitive" in photography ; at least in my experience. People often point 'n click cameras with hope, optimism, curiosity, earnest intent, and maybe a few other motivations but intuition doesn't come into it. The nearest I've seen is the aleatory approach where everything is shot incessantly and maybe something nice will be discovered on the contact sheets.
In my time as a gallerist looking at portfolio after portfolio from hopeful photographers I heard them say "intuitive" quite often but inevitably "intuitive" was a code word or excuse for: "I really like this picture but I don't know how I got it". "Intuitive" sounds a lot better than "lucky" but it amounts to the same thing if you shoot enough frames.
There are individuals who can, when standing at one perspective, easily imagine the scene from another and move appropriately. (If you know an architect, you will likely find that spatial intuition in that person as well) I also know individuals who can't see a damn thing unless it's through a viewfinder. And there are photographers who have a real knack for sensing what others will find effective.
Personally, I have a number of shots in my head that I haven't been able to take yet. We got into a lengthy discussion about 'previsualization' in this context.
Whether you call it "intuition" or imagination or something else, whatever. Semantics are less important than knowing that there is a big difference between spray 'n pray and what most skilled photographers do.
I have been at it so long, LF for over 70 years, that I suppose even the calculations are essentially intuitive.
I have been at it only half the time you have, Jim, but I agree -- the technical becomes intuitive after awhile.