Honestly, realism justifications for encumbrance outside of survival-type games where basic biological needs are the core gameplay loop have always been silly to me.... but the latter one about wheels of cheese rings true.

To me the argument is "what does optimal play look like"? Without encumbrance, there's no reason not to pick up every wheel of cheese, so optimal play is to pick up every wheel of cheese, which is tedious and dumb. But with encumbrance, every wheel of cheese becomes a tedious decision, and completionist-optimal play is to burn endless time ferrying stuff to the shops or storage or whatever. But as you said, making every wheel of cheese not something you can pick up breaks immersion.

So what's the compromise that actually makes sense for the "wheel of cheese" problem? A realistic setting is cluttered with "slightly-useful" items. Don't put so many "slightly-useful" items outside of settings with NPCs that will have realistic reactions to you stealing their stuff? But coding those realistic reactions ("uh, you're The Savior, I guess you can steal all my food... a bit... okay that tears it call the guards!") would be some more dev-work in these already-bloated projects.

But the problem still exists in hostile locales. A lived-in enemy camp is going to have store-rooms of "slightly useful" stuff. If the hero stops to raid the larder while massacring nameless Stormtroopers, is that a problem? I can see the immersion argument that "well, if you can, you probably should since you might need it and that breaks immersion" and therefore that justifies the encumbrance idea, but I also see Steph Sterling's argument "this is just a game and I wanna!" And I have trouble defending realism in these games about butchering your way across the landscape without ever stopping to poop.