What do you do that allows you to think critically and see the whole scene objectively before wasting film or megabytes?
I confirm the presence of basic building blocks like light quality, a subject I can isolate and prioritize visually, the ideal time window, and last but not least, is it even interesting.
Since I'm fully capable of identifying a bad photo, why can't I stop myself from pressing the shutter button when I see it in the viewfinder?
By all means, press it. Then look for something better. It's OK to abandon your original subject/approach.
Could it be that the greats like W. Eugene Smith somehow learned to quickly see each part of a scene and was able to decide if it was a good shot or not before the moment passed? Is this an ability that's just naturally present in some people, or do most photographers have to do some sort of rigorous eye training to get there?
You don't have to be a great. I do this, but a lot of the thinking is really forethought and anticipation. Light, you can evaluate constantly as you go. Go towards or stay in the good light. Manage your working distance according to your chosen focal length and the subject you anticipate, as you go. When I leave the house with a camera, I set the ISO based on the expected lighting conditions, and maybe the exposure too. What I know, I go ahead and prepare for, so I'll have as little as possible to think about when the unexpected happens.
You mention portraiture. Different beast with its own rules, but really the same building blocks.
For me it's down to trusting my taste, liking what I like, and elevating it when I find it. Other passions like sci fi contribute. Definitely other photographers ("What would Doug Menuez do?").
Also, watch this.