I'm always wary of game designers who espouse "balance" all the time. The only place you ever need balance is in a multiplayer game as people like be on an even playing field.
In single player games however, too much striving for balance can lead to a very boring game. One of the classic failures in this regard was Elder Scrolls: Oblivion. It had a balancing mechanism for all the enemies in the game, so that they leveled up in step with the player. However, this meant that every single monster was almost the exact same challenge, all the way to the end. ie. You may have leveled up and increased your damage output, but the monsters have increased their hitpoints and it still takes the same 3 attacks to kill anything. It removed all sense of progression from the game.
So it just goes to show that too much balance can really bore people! You need to hook a player and get them interested by giving them a sense of progression, of achievement.
Some ways that you can give a sense of achievement is by letting them work out optimal strategies, min/max'd character builds, etc. These can be unintentional or artificially included (eg. super weapons near the final boss fight).
tldr; People like a sense of progression, even if that is achieved by having an unbalanced game.
I don't quite agree with you here. I think Elder Scrolls is a bad example to give because the series as a whole is probably one of the most unbalanced RPGs there are: even in Oblivion, the 'balancing mechanics' you refer to just encourage more unbalanced play -- as opposed to, say, Galsiah's Character Development in Morrowind which is ultimately a balancing mechanism but promotes more aspects of gameplay and prohibits undesirable behavior.
Balance is best used as a function to encourage meaningful and difficult gameplay, which I'd argue can be defined largely as the number of interesting choices a player has to make. I think 2048 does a poor job of this relative to Threes: after around a week of play I was able to consistently win using the corner strategy. In Threes, the variance in tile distribution means there is no such panacea.
(That being said, I agree that pursuing 'balance' in a game is like pursuing 'colors' in an artwork. It's a road to reach some desired destination: not a goal in of itself.)
In single player games however, too much striving for balance can lead to a very boring game. One of the classic failures in this regard was Elder Scrolls: Oblivion. It had a balancing mechanism for all the enemies in the game, so that they leveled up in step with the player. However, this meant that every single monster was almost the exact same challenge, all the way to the end. ie. You may have leveled up and increased your damage output, but the monsters have increased their hitpoints and it still takes the same 3 attacks to kill anything. It removed all sense of progression from the game.
So it just goes to show that too much balance can really bore people! You need to hook a player and get them interested by giving them a sense of progression, of achievement.
Some ways that you can give a sense of achievement is by letting them work out optimal strategies, min/max'd character builds, etc. These can be unintentional or artificially included (eg. super weapons near the final boss fight).
tldr; People like a sense of progression, even if that is achieved by having an unbalanced game.