The reason people want class balance is because feeling like the 3rd wheel in a group sucks. Most D&D games spend 50-80% of the game in combat. There are some people who play with a lower percentage than that, but that appears to be the average.
So, in a 5 hour long session, knowing that at least 2 and a half hours of that time will be spent fighting things, most people want to know that they are doing something useful during that time. There's only so many times when it becomes your turn in combat that you can say "I continue hiding under the table until the wizard goes and kills all the enemies with his fireball" before you get sick of it.
Could you say the same for a 5th level magic-user taking out a 10th level fighter, even if they got a jump on them? I think the later is a lot less likely.
Yes, I could. They have a number of spells by the the time they get to 5th level that is a near guaranteed win in they were fighting a 10th level fighter: Hold Person is likely to win a battle if the magic-user goes first. So are a number of other spells. Depending on how high the fighter rolled for hitpoints a fireball could take him out. Stoneskin, I think, is probably 4th level, but I can't remember. It has the ability to make the wizard immune to nearly all attacks from the fighter for a couple of rounds. My knowledge of spells from 2e and 1e has dwindled in the years since I last played it. Charm Person pretty much ends combat and lets you control the fighter for a while.
I fully understand that we all want to be special flowers at the table with our characters, but should that not be more about character development and roleplaying than stat blocks? You can make your 1st level rouge just as interesting and fun as a 20th level sorceress with the power to level mountains. The rules should not try to force that, but rather compliment play to make sure you have fun regardless which class you try to play instead of sit around comparing die sizes all evening.
But what if your idea of fun is being the cool rogue who leaps over people's heads, trips the enemy and stabs them in the back, killing them outright and you aren't satisfied with doing 1d4+3 points of damage to one enemy while your wizard friend hits 10 enemies doing 10d6 points of damage to each of them?
You can roleplay the bad-ass rogue all you want, but when the rubber meets the road, the rules determine what you can actually DO instead of what you SAY you can do. And when those rules have the wizard waving his hands over locks you tried 10 times to pick and failed, only to have them open immediately....or those rules have you search a door for traps, not find any and then have your wizard wave his hands and discover all the traps in the room...or you try to sneak past some guards only to have them hear you(but not your friend the wizard, who has a silence spell up)...well, you begin to feel like it might be better to just be a wizard.
Sure, you can roleplay just as well as that wizard. But over half the time, you aren't roleplaying, you are fighting. People just want to be as good in both halves of the game.