I think it can aid in immersion. I also think they should have designed things around having a reasonable amount of shit to carry. You literally walk everywhere. Do all the protags have severe back problems by age 30? Because they're generally carrying way more than the amount that is known to do exactly that. How much crap a soldier can carry is an important calculation for the military, and for any survivalist. They should have looked for ways to simplify the amount of junk to lug around. Say by making item repair kits into *an* item repair kit, that you restock as needed when able.
Having to scavenge as you go along and be careful factors into combat, insofar as supplies are needed for it, too. So there's a strategic aspect to it as well. Now, figuring out what to do with all those stimpaks tho...that's a tuffy. But, I think it was Van Buren that planned to have some kind of caravan pulled by brahmin, so you could have a sort of mobile player home with mobile home level storage space. So that would be a good way to avoid the limits of human carrying capacity. You could work up a collection of stims while being able to have so many on hand for battle, or expeditions indoors/underground.