With dogs, is this just a 'top dog' thing? Or is it something else-- when a dog wants to be physically higher than other living creatures?

There has been a major misunderstanding, and scientists are to blame.

In the late sixties, Dr. David Mech studied captive wolves. He observed a pecking order, called it “pack theory”, introduced terms like “alpha” and “dominance”, and published his ideas.

“Dr. Mech himself has denounced dominance theory [...], and has admitted that he was mistaken. He has explained at length that his theory was flawed and that we should not be using it to describe wolf OR dog behavior, because both are far more dynamic and nuanced than was understood by the original dominance framework.”

(Source)

The reason we know this is that there have been studies done since – on wolves who live in the wild. As opposed to the captive ones, these wolves did not act like psychopaths, attacking each other over access to space or other resources.

So, this is a very basic truth: Your dog is not trying to be “top” when he gets on the couch. He’s up there for the same reason you like to be: it’s comfortable.

PS: In my experience, dogs absolutely understand space. More so than we do. If your dog were not aware of space, wouldn’t he constantly fall?

According to some Jack London stories, animals seem to understand how to “get their back up” when choosing a defensive position in a fight. Bison do it with their young when confronted with wolves. A moose or elk will back itself up against a tree or rock so the enemy has to confront only it’s horns or hooves. So taking the high ground seems natural enough for dogs.

“Why do they sometimes think they get the couch and the human find someplace else?”
My impression is that dogs who claim high and prominent places are (not trained to not do so, and) being self-centered, assertive, and/or pushy, as many dogs are – they want something so they rush to get it first. Same as with food or a toy or prey or whatever.

As for why they want a high spot, I haven’t got that impression from dogs. My impression was more that they like being in a good comfy spot (and there are some naturally good things about higher spots for most/all species) that lets them be with their people.

Also in some cases it seems some not-so-well-trained dogs who have been told not to go on a couch or bed, may still be wanting to push that boundary and/or start to get fixated on getting to go back there because they were denied it before.

I’m with @longgone, if my boy takes mom’s recliner while she does dishes, he just wants to sit there and be cozy. He does the same to me and my husband.

The only thing is, he must leave when the humans approach and ask him to get down. Any hesitation and he knows he’ll not be allowed there again. Same with food, you get greedy and beg, you get nothing.