There is no way they can be perfectly balanced even if someone wanted them to
And your "weenie" character idea is awesome
But "balance" here isn't the same as in a competitive game and maybe "balance" is the wrong word. It's about retaining the value of a challenge, giving meaning to tradeoffs, making choices meaningful and rewarding appropriate behaivior.
It supports the learning curve, heck, without balance there isn't one, or rather, it's not the same one as many elements in the game assume so if stuff is out of balance you can have a really strange experience with the game.
Take the old question of which is the "general puropse adventurer" class in this game, similar to the "no good stats" class you just proposed. The fighter class wasn't given any standout features just so it can be that baseline class (i speculate, and this was before the -10 XP per level requirements). Then a whole lot of stuff was made with the assumption that Fighter is the baseline.
What happened, however, is that this particular community ended up with the mindset that fighter was no good for anything. This was because the overall difficulty of the dungeons was much much higher (to root out exploity stuff). But the community, munchkins such as we are, took the dungeon difficulty for granted, and concluded that the Thief was, in fact, the baseline adventurer.
That thief was quite a way away from baseline because he brought in more powerups of all sorts into a dungeon (than any other character), and he effectively had double potions on every run. This was so generic, yet so powerful that classes and dungeons were being looked at and tested as "if a thief can beat it it's fine". Except that makes no sense because if the dungeons were tailored to the thief as baseline we'd have 4 powerups, and extra glyph and more potions per dungeon, and there'd only be one kind of potion that would restore both health and mana.
And it wasn't a matter of "fighter is just different" - fighter was strictly inferior to everybody by design. And the thief wasn't really unique - he was just playing a whole different game (or rather difficulty level). It's the same reason why a dungeon designed to challenge the Monk (Slime Pits) gets such universal hate from everyone - if a class is strictly more powerful then a challenge for it probably impossible to overcome by a class which is interesting, yet strictly less powerful. More or less.
But once a proper baseline was set and the game adjusted and stuff brought up and down in power the concept of full completion finally became an obvious option. For the longest while before that people were content if they could do 3-4 classes per dungeon for quests, and Vicious dungeons were talked about in "Which classes is X doable with?" terms. Once the "above the curve stuff" started getting nerfed some people were horrified - because they had unknowingly developed a "sub-Thief = unplayable" mindset (replace thief with whatever individual standard). Imagine what the classes look like to someone who latches on to say Monk, Warlord or Assassin in a world designed to challenge them?
Anywho - even if every class can provide a completely different and enjoyable experience, it's still probably a good idea to have them all playing the same game and be challenged as equally as possible. Some stuff will always be mechanicaly stronger than other stuff (except the theoretical guard class which I wouldn't mind seeing), but as long as everything else is not too uncomfortable or embarrassing by comparison it's all fine and dandy. I prefer vicious dungeons being talked about in "what are the best classes to complete it with first" rather then "did anyone manage X with anything except class Y and class Z? I just wanna unlock the dragonkin and play with it, guys, please help...
Err, srry for textwall.