Which is fine for a beginner, but has little to know use for someone who has read through the rules, seen a game played, and considered all the possibilites.
I disagree, and still think you're discounting one of the game's hidden strengths...simple example; in 3E town stats, you'll have a list of important people with sometimes little more than a name, a level and a class.
Of the three bits, the class is the most informative bit as to what this person is about, and that would no longer be nearly as useful if what you suggest was implemented. If you're feeling unimaginative, lazy, or unprepared, you can always default the NPC to the cliche of a cleric of that power level.
Additionally, beginners are gamers too, and not even all experienced gamers are as sophisticated in their character creation as you imply, especially folks like powergamers, who care a lot less about character concept than how many kills they can rack up, and at least a class gives them the bare minimum of a character handle for other players to hold on to if they don't care about it themselves.
I think where you are getting confused is the notion that a class as such has has any instrinsic ingame reality.
Eh? Sure it does. For instance, I make clerics church leaders most of the time, rather than rogues, who make better beggars. This has as much to do with class image as abilities. In theory, there's nothing to prevent a devout rogue from being church leader, or a luckless cleric from being a beggar. It just doesn't fit as well.
It doesn't; the different abilities the classes bestow do (a fireball is a fireball, someone taking an attack action with a bastard sword is swinging a sword), but the character's level in a class does not have any ingame, narrative significance.
To offer a counterpoint; power level has narrative significance, as implied by OD&D's suggestion of different types of gaming as levels increased (go dungeoneering, then explore the wilderness, then get a small realm, then ascend to godhood etc.), or the differing campaign themes of "Epic" level play to, say, a 1st level party. More changes than just the kobolds getting bigger.
The 'flavor' that DnD provides comes from ingame options which the entire group is privy to, not through class progressions. The narrative development of a pc's skills should reflect the particular campaign history and/or what the player wants out of it.
Which leaves those of us who just want to get their Conan or Merlin clones to 20th level out in the cold a bit. Luckily, D&D caters for just that in it's default state, and if you want more, you can build on that foundation, and make your barbarian completely different to all the other Conan-a-likes, and your wizard far more interesting than just another a pointy hatted Gandalf clone. The foundation can be ignored, but to remove it entirely would be a mistake, because a lot of us like to either default to it or build upon it.