Because how you played the tutorial affects your character. If you play through one time as a mage character, then the next time you want to be a warrior, your starting stats and equipment will be off (a mage wouldn't have picked up that warhammer and armor set, while a warrior would have; a mage may have picked up the alchemy equipment and magic staff, a warrior wouldn't have). Also, the first few times you play it, you likely don't do so well, so you'd have to replay it multiple times before you could get a good, balanced run-through.
If you're not picking up and using the parts that the tutorial tries to explain, how does that differ from a "skip tutorial" button? Automatic pickup of what you wanted? No, if so, do the work. You start out empty, and you have room to pick up much of the stuff, no matter what kind of character you set out to become. What happens during the tutorial will not affect you in a great way throughout the game.
Have you tried minimum difficulty and just fistfight your way out in a hurry? Can't get much cleaner start than that... As clean as a Morrowind start... Sorry, I just don't buy the explanation for not using the exitsave