Voted "They should not let health or mana regenerate", although with a major twist - the three split bar system:
Health - Lower : Critical wounds. You simply cannot heal these, not even by magic or potions. However they are not frequent to get. Increases also very slowly with sleep deprivation.
Health - Middle : Available Health pool. These can be healed in any number of ways, incl sleeping, but does not regenerate.
Health - Upper : Stun damage. If you miss the nail and hit your hand, it hurts like hell, but it's not a health issue. This regenerates automatically.
Mana - Lower : Permanent damage. Includes damage spells. Increases also slowly each time you cast a spell, but cannot be regained with potions or absorb.
Mana - Middle : Available Magicka pool. The amount of magicka points you have left, after subtracting the lower and upper part. Does NOT regenerate automatically, you need potions, absorbtion, or sleep. With Atronach, you don't even regenerate while sleeping (like in MW).
Mana - Upper : Temporary damage. Include drain spells. Easy indication of what you will regain when effects is complete. This regenerates automatically.
Fatigue - Lower : Permanent damage. Includes spell effects. Increases also slowly by not eating. Allow it to top, and it starts affecting health.
Fatigue - Middle : Available Fatigue pool. Good indication of how much damage you will do with a weapon. NOTE!! May not be higher than health.
Fatigue - Upper : Fatigue loss. When you do something, this increases lowering middle part. This regenerates automatically.
Effects of drinking appropriate potion:
Health - Increases Available Health pool, but does not affect Critical wounds or stun damage (stun damage fixes itself quickly, it's used for KO).
Mana - Increases Available Magicka pool, but does not affect Permanent damage or temporary damage.
Fatigue - Increases Available Fatigue pool, and acts as a power drink to temporarily reduce effects of sleep deprivation.
Effects of sleeping:
Health - Does not repair damages from critical wounds, but heals everything else incl effects from sleep deprivation.
Mana - Needs a restore if everything is to be fully regenerated during sleep. Otherwise permanent damage from damage spell will remain.
Fatigue - Restores everything except Permanent damage caused by severe lack of nutrition. Pays to eat before sleep.
Effects of eating:
Health - None except the secondary effect of not loosing health as quickly as when you were starving.
Mana - None whatsoever.
Fatigue - Reduces the effects of starvation, depending on the quality of the meal.
Duration of sleep:
Depends on your restoration (regenerative) skill and quality of bed. I'd expect a few hours in your own mansion bed, and several days in a sewer.
Perks:
There should be perks available for those not wanting this level of survivalism, where certain things are handled more automatically and conveniently.
Level:
As you grow more experienced, the bad effects limit themselves, but never go completely away.
Keep in mind the early levels are said to increase rapidly, so there should be plenty of time to get the perk before you even start getting annoyed. It's not supposed to end up as a "sleeping fest", more a "something to keep in the back of your head before going to a potentially fierce battle". I mean, if you show up starved and deprived of sleep, it just makes sense that you should be punished for it, right? In Blade of Destiny, you had no regeneration, and you only gained a point or two per night of sleep. Do you want to assist the guy hurt along the road? Makes a pretty important decision now if the spell cost 4 points requiring more sleep, doesn't it?
Lastly, this need for sleep artificially helps game time advance. At normal difficulty, it always feels weird being around level 40 after three months. Waiting could have todays interface, but sleeping should have a more convenient one, where you simply see time speed by really fast.