No. Just.. no.
Serious immersion killer and would make the game needlessly convoluted and annoying.
Wait,
that's what would be immersion-breaking? A system that reflected what someone could carry in a far more believable manner? I think you've got it backwards...
The thing is, a lot of people are referring to the fact that it's a fantasy RPG, using that as an argument against a system that did more to restrict how much could be carried; 'it's not meant to be realistic...' The problem with this logic is that there's a difference between realism and
believability. A game can have as many elements of fantasy as it wants, but things still need to make some sense
within the context of the game world. Unless there's some explanation for how
volume is completely irrelevant in the Elder Scrolls universe, or how it would be possible to change one's armor in a split second while in the middle of combat, etc., there's a problem with the current system.
As has already been suggested, real time animations for various actions would solve the problem of changing armor or drinking potions in combat -- if the player had to select those things from their inventory while events continued, and then wait for a few seconds while their character drank a potion, grabbed a weapon which hadn't been equipped or changed their armor, it would be pretty difficult to do while under attack. To anyone who would object to that, I'd say it's time to evolve with your games. I mean, if you're looking for an immersive experience, why would you want something as 'video gamey' as instant switching of equipment? What good are all these advancements in technology without more sophisticated gameplay?