If you want immersion, go to bed for 6-8 hours, and 2-3 times a day, drink water or a restore fatigue potion called water, No jugging healing potions, pretend to poop, etc. You don't need a game mechanic to force one to do those things.
I would argue that the user interface telling you that your character is hungry does not help you identify with the character or his situation.
In New Vegas, you never really feel it, see it, or sense it in any other way than through the user interface telling you, and being quite literally "told" by your pip-boy that you are hungry instead of having an actual immersive game experience where you interpret your characters' hunger through sensing it from his behavior or composure, or some other way that even I haven't thought of.
This might be a strange argument but I'll give it a go.
I would argue that eating food is to some extent instinctive. You feel hungry, you try to find something to eat.
Some people on the forums have said that eating is very important, much like dodging a strike directed at your character. Well how is it that I am never told when to dodge a strike. It is simply because know how to do that (even as a player it is instinctive), if I was told "Uh-Oh! You better dodge now!" Before being hit I would find that to be annoying, and even feel like I wasn't really "in" the game when that message popped up.
Now, you spotting your characters' hunger without any aid of the user interface will be very hard, your characters breath might smell worse if he hadn't eaten in a while or you might hear his stomach growling. That might be a way of spotting hunger in-game without it really pulling you away from the game. But other than that, you would almost need to medically examine your character to see any signs of hunger manifesting physically.
In fallout New Vegas that message is sent out by your pip-boy that constantly monitors the state of your body and tells you when you're hungry. In real life such a message would not be needed, you instinctively know that you are hungry when you are. For obvious reasons you will not have a pip-boy in the elder scrolls, and the invention of a hunger-monitoring device or magic would seem quite redundant in a world like Tamriel. I would however think that having your stomach growling in-game would be rather amusing, especially when sneaking your stomach would growl and expose you to enemies in a cave. This is something that might realistically happen, and I think this would be the only actual way of implementing it without making it "pull you out of the game" so to speak.
However I don't think dieing from hunger is ever really funny or immersive, and I find the idea of dieing from hunger when your inventory is full of food to be quite simply idiotic. Of course you can blame that on the player not paying attention, but I can't personally feel the NEED to eat and I don't feel the imminent consequences of not eating properly.
Edit: So basically what I am saying is that I'm fine with realism as long as it's realistic realism.
You two just read stuff below.
This is a split question. In terms of game mechanics, I love tons of realism. That's why I always download the Food mods, Hunger Mods, Thirst Mods, Sleep Mods, etc ... because Bethesda included thousands of items to discover in the game that are essentially worthless in terms of monetary value, and I hate finding all of that crap when there is no use for it in the game. However, a bedroll becomes important when you need to sleep. A frying pan becomes important when you must cook your food to eat. Apples and small fruits and vegetables become important when you're hungry but don't want to cook something just at that moment. All that luxurious food added to the shops and stores now has a purpose in the game. I love it when everything has a purpose, so I need those REALISM mods to give everything a reason to be there.
Edit:
To all those who don't want HC mode.
People, don't be egoistic and think of how that mod is optional and is not forced on you.
It could make many people happy so don't just talk trash about it only because you won't use it.
Also, everyone is making too big of complication and philosophy out of this.
Why should there be 3 meals a day?
Who ever said that human must eat 3 times a day?
I get with one meal a day perfectly fine for example (witch is maybe a reason why I am not a fatass like lots of people).
Also, there are ways to improve hunger, thirst and sleep need while in the game.
Hunger could make stomach growling noises, thirst could make small dizzy effects on the screen and sleep could do small blur effects on of the screen.
At start you will have no penalty, but as the time goes, you will start to get penalties like loss of fatigue and some attributes and eventually to your health starting to drain and you die.
Still, serious penalties like major fatigue and attribute losses and shouldn't happen until some time passes by.
One week without drink should cause death, four weeks without food should cause death and if you go without sleep for a week, you will fall on the ground and sleep for 12 hours or so.
By getting those penalties little by little, you will notice something is wrong with your character and have enough time to fix the problem (if you can't get your character to drink a thing in a week, then you really deserve to die).