Game balance is the hobgoblin of the D&D designer's mind. It's a shiv to the ego's gut, a reminder that even the best design will spring a hole. While balance has always been an issue, it's really important when you look at D&D post-2e's splats and skills and power. That's when players had enough choices, and enough control over those choices, that they could easily build huge gaps in power between them. You could build broken characters in earlier editions, but the DM (by design, IMO) had a lot more power to reign things in. It's a lot easier for a DM to say "Your wand runs out of charges" than "The wand is out of charges, you can't buy it anymore, and that feat you're using is gone."
A lot of gamers really don't care about game balance, and that's OK. A lot of DMs have learned over the years to fiddle with the game to keep things even, and that's a godsend to many designers. Your audience is trained to forgive mistakes!
There are also plenty of players and DMs who have no use for game balance. If things are out of whack, their playstyle is such that it doesn't matter. Who cares if the berserker can kick anything's ass in melee, if the campaign is a mash-up of Romeo and Juliet crossed with The Longest Yard. Fighting isn't the point, so all those unbalanced fighting abilities the berserker uses don't matter.
If you do like combat, though, then game balance is very important. A DM needs the system to provide some framework for building encounters, or at least judging their difficulty. If each class has wildly different combat abilities and the game doesn't account for that, the system falls apart and the DM's judgment and experience have to take over. That probably means lots of trial, lots of error, and hopefully a patient enough group that a DM learns to balance the game using his own set of metrics. Of course, if a few PCs die and classes rotate in and out of the group, the balance act starts all over again.
So, some players and DMs don't care for game balance, but others want and need it. In fact, a lot of people want it. And the really nice thing is that a well-balanced game doesn't take anything away from people who don't care about balance, while making people who do care about it happy. The key is making the people who don't care about balance happy, and that's another bundle of trouble.
A well-balanced game means more than simply making all options equal. A well balanced game offers a lot of distinct choices and vivid options, without *needlessly* restricting them. That's really the trick - where does that needless line rest? 4e catches a lot of heat for this. For some people, wizard spells that obviated skills were bad because they replaced rogues in those critical situations where the rogue had a chance to shine. Others didn't care, or rarely had rogues in the party, or had enough chances for the rogue to shine that the wizard didn't steal them all.
It's a tough line to draw, because D&D is really a large number of games placed under one umbrella. Some people like lots of combat in their D&D, others enjoy free-form roleplay with teh occasional die roll. To attempt to distill D&D down into one experience that makes everyone happy is difficult.
In a way, though, game balance has to draw lines and partition things. Game balance exists at least in part within the context of a specific campaign. When you try to balance the game, you have to create a sort of platonic ideal of a campaign and work from there. Do some people think it's cool that wizard spells make skills worthless? Sure, but that might not be the baseline you design to.
Balancing D&D is hard and boring. Few people will thank you for it when, by some miracle, you get it right. Everyone will tell you how you've messed up, either by nerfing things, making things bland by balancing them, or taking away toys they liked playing with. It's precisely the job that designers are paid to do so that individual DMs aren't stuck with it.
At the end of the day, though, if you balance the game just right everyone's happy. The guys who don't care about balance get lots of options and toys to play with, because you picked the right lines and didn't take away stuff they liked. People who like the challenge of breaking the game work harder to bust the game's math. They have a steeper mountain to climb! The players in the middle get to have fun picking options based on what looks fun, interesting, or that fits a character concept. You're not stuck with a lame character because you think it would be fun to play a samurai. DMs get to run engaging campaigns without taking on too much work that the designer left for him.
So, that's why designer should keep tilting at the game balance windmill. It's hard, rarely rewarding work, but that's what we're paid to do. We take on the tough, boring tasks so DMs can spend their time doing the fun work of running a D&D campaign.
My homebrew 5e DM Screen
14 minutes ago