Exactly!
For me D&D is not a competition, but I am not against some other group thinking of it that way...
It isn't really about competition for people that are after balance either, at least not usually so.
If it was just competition, then it would be okay, we'd just all play Wizards and CoDzillas and try ot make the most uber character we can.
I would classify it more as "contribution". We do not want that the choice of a particular character class automatically means that character has less to contribute.
If it comes to, say Travelling, you have a Fighter. In 3E, he could train Climb, Jump and Swim, which is pretty useful for traveling. But the Wizard could fly and teleport - possibly the entire group. That means the Wizard is better than the Fighter alone for traveling, and if group abilities are used, the Fighter's ability is even superflous.
Take Combat. A Fighter has the best attack bonus, the best armor and the best defense. A Druid has his animal companio nwhose stats equal that of the Fighter or exceed it, and he can still cast spell or wild-shape.
Chosing the Druid allows you to contribute as two Fighters. Chosing the Fighter allows you contribute as... one Fighter, not surprisingy.
Now, there are other reasons other than mechanical balance why one player contributes less and one player contributes more. Someone may be shy and rather hold back, rarely adding. Another player may have no sense of tactics and make the worst mistakes. And yet another player is sleeping with the DM and gets everything he wants anyway, or whatever. Those reasons are their own "problems", but not one that the game mechanics can fix.
If we don't want to give the Fighter the ability to teleport and summon animal companions, and the Rogue the ability to cast Silence, Invisiblity and Knock, and we don't want to take these abilities away, there may be other ways than 4E. But they'll probably be heavily meta-game focused, like giving the Fighter and Rogue "Karma Points" or "Bennies" or "Possibilities" or some other metagame resources which they can use to bend the rules for their benefit. Say spend Karma so the Fighter can say "No, I can't teleport, but I once worked as body guard for a local Wizard and he still owes me a favor or two, I think he can teleport us wherever we want" or the Rogue may say: "Oh, I think I remember the kitchen servant of the BBEG, she can smuggle me in, so we don't need Invisiblity" or "I just spend Karma so the enemies ignore my failed stealth roll".