You seem to be assuming that immersion and enjoyment are opposites, that inceasing immersion will somehow decrease possible enjoyment of the game.
Not at all, not in general, i asure you ...
I see it more like a seesaw ... immersion on one side ... fun on the other ... enjoyment would be amount of happyness you have on that seesaw.
If you dislike the word feel free to either switch "immersion" to "immersive fun" and "fun" for "unimmersive fun", "nonsence just for the sake of fun", "crazy stuff", "havoc", or anything else that brings people fun WHILE it dont also brings immersion (that is important part, not the fun word).
The more seesaw is tilt to the "immersive" side ... the less "unimmersive fun" you have ... so *full* immersion would be one option ... you would need to manualy walk everywhere, you would need to eat, sleep, drink, pee, poo, rest after certain amount of traveling, reading would take real time, weapons and armors would need to take care of, otherwise they would broke ... i hope you get the picture, the closer to reality the better.
Such game would be quite a drag for people like me, or Icelyn (i dare to presume, pardon me if i presume incorectly) ... but that doesnt mean nobody can enjoy it, i know many people who enjoy incredibly thorough survival simulators, im simply not one of them.

Second option would be seesaw on the "unimmersive" side ... that would basicaly mean no immersion at all ... i cant quite imagine such game to be honest, but i believe things like Fortnite would be quite close ... and (even tho i dont quite understand it) they are also popular and some people enjoy them.

Of course from elementary geometry we know that there is infinite amounts of settings "in between" those extremes ... i hope we can agree on this.
But the third common would be 50/50 ... or more like "somewhere close" around that.
In general you could say that rules are not utterly nonsence but also arent exactly real world simulator ... or my personal favourite description: Game provides healthy amount of rules to make sence, while not being overwhelming by them.
Yes im aware that some people would have that "perfect experience" in 20/80 ... 80/20 (yes, there is difference) ... or litteraly anywhere else, once we include decimal numbers, we are heading to that infinite amount of options.

And there are ALLWAYS people who would enjoy the game, no matter in what position the seesaw is ...
So, coming back to that original statement ... in some point of wiev ... it may seem that way:
Yes, you could say that incerasing immersion beyond certain point starts to drain away the enjoyment for certain people ... on the other hand decerasing the immersion beyond that same point starts to drain away the enjoyment for other people ... and keeping it on the same point will piss off everyone who dont have set his own prefferences exactly on that spot.

Basicaly Larian provided their balls, and now we are only deciding who shall stomp on them.

For example, how would the game be less enjoyable if weapons were carried realistically, or if there was a passage of time?
Good question!
(i say it bcs i would probably give it too, if i would be on your side of this baricade

oh wait ... i did, just other way around.

)
I shall take it in backwards order, since time is easy one.
Even tho ... it depends on what are you meaning by "passage of time" ...
- It can be interpreted as timed events ... you take the quest and since *now* you have *XY* days to deal with the problem.
Some people (and i say some people just bcs i dont want to name Icelyn again) allready expressed they disliking for this, and i kinda understand her ... i mean them ... since you can easily get lost in sidequests and exploring and forget about that there is only *XY* days to save the Grove.
If that happen to you, it certainly can be source of frustration ... specificly the grove can be quite harsh pusnishment, since you loose a LOT of quests, at least one (but up to 3) vendor, and other stuffs (like loot, lore, etc.).
Frustration allways sucks ... i hope we can agree on that.
Even tho, just for the record ... personaly i would welcome timed events, since i belong on the other side of spectrum ... i dont mind loose single quest, bcs i get to fulfill another, since i would replay this game several times anyway ... so this way i would at least have even more distinguished experience for each play.

- It can also be interpreted as regular time flow ...
The way we know from Elder Scrolls, or Fallout series ... time flow, and the world reacts ... during the day all works as usualy ... in the night, people are sleeping, shops are closed, city feels empty until you enter some house and if you do, you are usualy attacked on sight.

That kind of stuff ...
That sounds immersive as fuck and i believe that many people would welcome such thing.
Not myself tho.
While idea of night attack while people are sleeping and murdering everyone rather than battle them is tempting ...
I hated it in both Elder Scrolls, and Fallout games ... i come to town to trade, gain or finish my quests, there is not much other reasons for me to get there really ... and every single freaking time i fast traveled to the city ... i emerged there in the middle of the night, when of course none of it is possible. -_-
And the idea of need to spend valuable rest resources just to make this freaking city to work as a city ... seems horrible to me.
- It can also be interpreted as purely cosmetical time flow ...
Much less immersive than the one abowe ... on the other hand, much easier to enjoy im my personal opinion.

So thats my "how" for time passage ...
As for weapon carrying ...
This isnt really matter of any enjoyment since i believe it should be called estetical prefferences.
The more you like visual of something, the more you enjoy it ... i hope we can agree on that one.
My personal opinion is that we should get options.
Just as we do with helmets ... option to hide helmet is also "unimmersive" ... and yet it was well received, i dont recall even single person mentioning it ruined his game. O_o
I cant honestly say anythng much deeper about how would "realisticaly carried weapons make my game less enjoyable" than simply say that i would like the look to my characters less ... thats just it.
What i can say tho, is that it would make the game MUCH more enjoyable for me ... if my Paladin could wield his sword on his hip ... while my Ranger would have there quiver with arrows, or bolts (same reasons as you are using for meele weapons) ... while my Rogue would have no visible weapon on himself, since his daggers are actualy hidden inside his sleeves ... while my Wizard would be allways leaning on his staff.

Oh that would be a very nice sight for myself indeed, and i would enjoy looking at such party much, much, more ... than the same that just "realisticaly carry their weapons".

I think that in general, if done right, improving immersion will improve enjoyment.
Thats bcs "if done right" is basicaly a condition that fulfills itself. :-/
You could aswell say "it would be better to do better" ...
And of course you think that ...
You want more immersion in the first place, its quite logical that you presume it would improve enjoyment ... why would anyone "want" something that would make his enjoyment worse?

I will give you that in some cases improvement of immersion versus enjoyment is debatable.
Glad we can agree on this.

//Edit:
OK, but in combat everyone is holding their weapons, right? And in combat they are climbing, walking, running, falling prone, jumping, falling, attacking, blocking, taking hits, casting spells. So the animations are already there.
Im affraid not ...
I dont say im sure right now, but i believe that our characters sheat their weapons for some of those animations ... climbing and jumping im quite sure they do ... not so much about the others.
It would just be a matter of having people hold on to their weapons outside of combat.
I believe i allready mentioned it here ...
You can keep your weapons unsheated all the time by pressing Tab (default ... i believe the hotkey is named "toggle combat")