It is not an exaggeration to state that I have not sat down to listen to this record in its entirety in decades.
It’s interesting because listening to just the singles is a vastly different experience than following the story in context. The context which is dark and deeply sad. When I found The Wall as a teenager unfamiliar with the concept of a concept album, I remember not just hearing this album, but feeling it. Feeling it in a very different way from other records I had encountered to that point. In those days I’m not sure I knew much about the story behind the music, but I knew that it was emotionally moving.
The Wall is heavy in a way that I can kind of understand how it fell out of rotation. Not because I don’t love it, but mostly because it’s hard to listen to a story so achingly sad. I feel similarly to Like Clockwork from QOTSA. I love that record. Indeed it’s possibly my favorite, but the complexity of the emotions found between the grooves sometimes makes it a tough listen. All that said, The Wall is a beautiful piece of work. Sitting here now, with a few more decades of life behind me, much of this record resonates in a different way.
Maybe that’s the beauty of it.
Vertical Separation 
You have to be right. This album, I think, requires an adult’s perspective — it was written from one, of course, with all that experience interpolated on children’s sort of naivete. Which doesn’t undermine your points about its being uniquely heavy and sad.
This fell out of my favor as well, though for somewhat different reasons: I found I had a hard time with the ‘whining’ — as if his semi-charmed life was the only one with difficulty (the man still has this chip on his shoulder).
I do think, however, this movie has the absolute best analogy of what the education system is like: the scene with all the masked kids marching in lockstep into the meat grinder to emerge identically ubiquitous and interchangeable.