There is one big glaring deadly reason why it's a bad idea to institute a penalty for sleeping in armor.
First, as others have said, this only penalizes characters who wear heavy armors. The heavier the armor, the worse the penalty. Someone wearing medium or heavy armor has to weight the consequences of being very vulnerable if a fight breaks out while they're sleeping, or eating the penalty all day tomorrow, but someone wearing light leather armor will take it off at night, and only be short a couple AC points if a fight breaks out.
OK, now for the glaring deadly flaw.
In 3e, party resources were very much the resources of the entire party. If a rule penalized one or two party members, then the party burned resources to fix the penalty. For example, a fighter who is fatigued the next day, or begins the day wounded, is fixed by the cleric casting the appropriate spell - now the cleric has burned a spell that could have been used later to save someone, anyone, in the party. Net result, the loss of a spell that could have benefitted the party.
If an unarmored fighter must fight unarmored in the middle of the night, he will take more damage and the cleric will have to use more of the party's precious healing resources to heal him.
But in 4e, resources are more individual. A fighter who is fatigued the next day, or begins the day wounded, must expend his own resources (healing surges) to fix the problem. Making him start out with fewer healing surges has the same effect. Net result, the loss of an individual resource that could only be applied to this individual anyway.
If an unarmored fighter must fight unarmored in the middle of the night, he will take more damage and then he will have to use more of his precious individual healing surges to fix it, leaving him personally depleted of healing surges while the party as a whole is not.
The real difference here is whether you're penalizing the party as a whole (3e) or penalizing one player (4e).
A rule that reduces overall party resources creates a challenge for the party to overcome. Can they spare the cleric spell in the morning? Maybe they should chip in, out of party loot gained, to buy or barter for a ring of sustenance for that fighter so he won't need to sleep? Maybe they should just make the fighter sleep in his underoos and work together to protect him if he has to fight in the night.
But a rule that penalizes just one individual makes him weak and vulnerable. It singles him out. It punishes him for his choice of class.
While a penalty for sleeping in armor might be a more realistic approach, we have to ask ourselves if we want a rule that is so lopsided that certain players will be punished for their class choices while other players are not.