Plenty of other games do a fair to fine job of including the sorts of animations the OP speaks of.
METRO games call it “holstered” and have a button for it, at least EXODUS, but they might also have a time-delayed idle trigger for it. For handguns I think it does actually holster them, while the long gun in the player’s hands will just be held down and away, relaxed, rather than being permanently shouldered at the ready. I forget whether the STALKER games had a separate button for it, but the NPCs in those games DID take offense to you pointing a gun at them and reacted much better if you at least put your gun away and swapped to your binoculars or something less threatening to speak to them. Those were effectively FPS games, similar gameplay perspective as GZ.
Likewise for NPCs in the Elder Scrolls titles—Morrowind, Oblivion, Skyrim, etc. Same, again, for the Fallout games. Better off talking to them with weapons put away, and that meant sheathed, holstered, slung… Those allowed for both first and third person perspectives, at least to an extent…
The Division games have both a “holstered” state (inside safehouses, etc) and a “down but ready” state for when the player is just wandering around and isn’t in immediate danger. Those are pretty much pure third-person shooters.
Pretty sure the Army of Two games had holstered and relaxed states.
The two most recent Ghost Recon games have relaxed states as well, with the weapon down. I think it doesn’t work in first person mode, but does work in third person mode. I forget if those games also have separate holstered states.
Getting these holstered and relaxed states to look right is just a matter of scripting and animation work. It IS a lot of work, but it really isn’t or shouldn’t be terribly difficult… It’s just a matter of whether the devs themselves consider the added immersion to be worth the time and effort to animate and script.
In reality, even a soldier in an active combat zone, even immediately under fire, does not always go around with their weapon shouldered. It is very difficult to move around, with some weapons, if it is constantly held up, shouldered, at the ready. You can’t run well, you can’t navigate narrow passageways well, you can’t enter and exit vehicles like that, or slip through narrow gaps where debris renders an otherwise easily traversed passageway or street/alley partially obstructed, etc…
Echo, I love that example from DOOM. Doom guy’s arm has been thrust through the camera man’s chest, to put the gun in that position…