While I don't disagree with your assessment of cover, I don't think it is particularly useful to hang on to a pedantic definition of "circumstance modifier" for the purpose of the discussion.
Calling using "circumstance modifier" correctly, as a term that means a modifier based on the actual circumstances (like it sounds), as opposed to a modifier based on other factors like skills/traits/powers,
given its demonstrated history in D&D specifically (as well as other games, including wargames), "pedantic" seems a lot like special pleading to me lol (or like someone has mentally blocked all memory of 3.XE D&D, which I can understand I guess), but you do you.
And the point remains, D&D 5E combat's default RAW approach has an extra step (check for cover, apply penalty if there), just one that's broadly ignored, and I think that is very relevant. If people took cover seriously, it could pretty quickly get annoying as in more cluttered environments indoor environments, forests, etc. and ones with PCs giving to cover to monsters and so on (and creatures explicitly do give cover) you'd virtually always have a cover modifier on ranged attacks, and somewhat frequently on melee ones. And even when you didn't, you'd often be considering whether it should be present.
But I've never seen nor even heard of anyone actually running it like that.
The most onerous resolution steps in my experience tend to ones involving:
A) The requirement that someone assess a situation to determine whether something applies. Especially if that thing has a potentially variable value like cover.
B) Math - especially subtraction.
C) Any kind of choice (like PbtA's choices, or Cortex's choice of dice, or systems where you have to "allocate" successes to different things)
You can really quickly escalate a simple/minor step that's not a problem into a really tedious one by adding some or all of those factors.
Or god help us:
D) Where resources can/must be allocated after the fact to influence success/failure. I'm struggling to think of a system that does this routinely (as opposed to only via abilities, Inspiration, etc.), but I know I played something where we basically had to roll then "pay", and people trying to work out how much to "pay" was a major brake.