Related to the inherent difficulty in seeing, in any kind of completist way, what we're looking at we seem to suffer from a deep desire to simplify what we look at. Perhaps it has something to do with the need to see the tiger rather more than the forest. Regardless, we're constantly simplifying and summarizing as we look around ourselves, extracting what we think are salient elements, "my wife" "a boat" "a fire hydrant."
A finished photo is typically both small (relative to the world) and persistent, static. We take the thing in in all its detail (ok, maybe not quite all, but some). We take in the details more readily, in any case, than we do the details of the world. The commonest mistake in photography is to see Grandma and to miss the background, which background becomes glaringly obvious in the picture, later. Photographers deal with this is myriad ways, mostly harmful.
The more sophisticated photographer seeks to solve this problem not by looking at the background particularly, but by controlling it. One "checks" the background, one does not look at it. Place Grandma against a blank wall, a painted backdrop, or simply open up to f/1.4 and drop the whole thing into an incomprehensible blur. The background problem is solved by eliminating it, rendering it irrelevant to actual seeing.
Lighting is treated, often, in much the same way. You simply move the lights around as shown in the diagram until the shadow under the model's nose matches the diagram. When you're attending to the shape of the shadow, it is incrementally harder to attend to the model's expression and body language.
Much of photography as it is actually practiced by more or less serious practitioners is simply pattern matching of this sort. Do this thing until whatever you're looking at matches the diagram. All compositional tricks follow this template, the rules of thirds, leading lines, and so on. You simply move yourself or the subject around until the pattern is matched, and then you press the shutter. It becomes almost unnecessary to actually see what's in front of the lens.
That sounds rather flippant, but let us review that seeing what is actually in front of the lens it remarkably difficult, it is no mystery why we seek frantically for shortcuts.
Allow me to draw a somewhat artificial line. There are perhaps two schools of photography, one of which seeks to simplify the thing in front of the camera until it can be more or less "seen" while photographing it. The other seeks to find some sort of essence. Ansel Adams talks about an authentic emotional response, but is silent on rules of composition. Naturally, in the real world, one partakes ideally of a bit from column A, and a bit from column B. There's certainly nothing particularly harmful about isolating a subject, if that makes sense. There's nothing inherently harmful in moving lights around until the shadows land in the right places.
The harm is when, by paying too much attention to column A, you lose the things in column B. Column B, that essence, the emotional response, that largely indefinable thing which you only know when you see it. I submit that it's column B that matters more.
When I take a picture, my aim (rarely executed well), is it first feel it, to first get a firm grip on what it is I want to photograph, what matters here, what is the essence. I try to see, if not fully, at least thoroughly, and grasp what I am seeing and what I think about that. After that, I move and wait until there is at least some slight compositionally fortuitous arrangement. Sometimes it works pretty well.
This is basically the process the Miksang people talk about, but it is also arguably Light, Gesture, and Color as well as innumerable other sources.
Column B first, then column A.