I am not a degreed engineer, in fact I am a public high school graduate, my only formal education beyond that having been a 38 week electronics school in the Navy. I do however understand what you are saying. I have done a lot of projects which I constructed mentally and then recognized the flaw in my plan and reconstructed mentally before actually starting the physical project and without putting anything on paper. I did maintenance on small offset printing equipment for thirty or more years and I can still visualize one of those machines as if it is on a movie screen in front of me. I can start it up, see the parts move and even section it to see the internal parts and tell you which are moving clockwise and which counterclockwise. If I really concentrate I can “hear” it, not as clearly as I see it but I can still bring it back. Apparently most people are unable to do this. I used to do the “celebrity cryptogram” in the local newspaper and reached the point that in many cases I could look at it for a while and then read it off without ever picking up a pencil.
You are right that most people lack the ability, I am the same way. However as I get older I’ve found it more and more difficult (not impossible) to perform those visualizations. I don’t know if I can attribute it to just age or the various alcoholic beverages I’ve consumed over my lifetime. I live a very healthy lifestyle and I know that helps but it is very unnerving to feel like a treasured skill may be waning.
The ability to visualize the entire system has prevented so many coding disasters over my career I couldn’t count. Hopefully you don’t experience the degradation like I have but unfortunately it might be a unavoidable certainty.