Save right before the exit where it lets you change everything on your character, so you only need to do the tutorial once. :shrug:
Lets you save everything about your character... except what you picked up. A warrior wouldn't have picked up the bow as a starting weapon, while a stealthy character might have. An assassin or mage may have picked up the alchemy equipment, while a barbarian wouldn't have. Also, for a first time player, you may not feel that you did that great a job when you first reach the exit, so you wouldn't want to use it as a starting point for replays.
I didn't really like Morrowind's (non-existant) tutorial the first time I played. Even though I had played Oblivion quite a lot by then, starting out in Morrowind just overwhelmed me. I didn't have any idea what I should be doing, beyond the get-to-Balmora objective. I didn't know what kind of equipment I would need (ie, what do I need now to keep from getting killed, vs what would be good to get later), and there were
three ways to leave (the one path through the swamps past Tarheil, the one through the foyada, and the Silt Strider).
On the surface, Oblivion's was good, but upon retrospection, there are problems. First, it was a bit too long, which, although there was that great sense of awe once you got out the first time, it made subsequent replays annoying (Oblivion was my intro to TES, and I can't count how often I had to restart a character because I just wasn't getting the hang of it). Second, it didn't (couldn't) assume anything about your character, so it was throwing all different types of items at you and encouraging you to use them regardless of your character type (alchemy equipment, bows, daggers, lock picks, hammers, etc), it always starts you off with some spells, and at one point even encourages you to be stealthy even though you may not be playing the appropriate character type. That really messed me up in the beginning, because even though I was playing a mage character, I was being given non-mage items like I would require them, and being asked to do non-mage tasks like I had to do them to advance.