I voted that it was very important. I have had many a 2nd edition game ruined by lack of balance. The issue is with expectations. When, as a DM I can not longer assume certain things about the powerlevel of the group, the game falls apart.
The best example was a game in 2nd Edition where a player extremely powergamed his character. He used the Skills and Powers rules to make up the best combat monster he could, and I said it was fine because he had to take a lot of disadvantages to get those powers, so the game was still "balanced". Or so I thought at the time.
I figured that if his character had to be pig headed, arrogant, beligerent, and a jerk to make up for his fighting ability that he'd be dead in no time. I started the game at low level and had a high level fighter bump into his character to prove a point, knowing that if he played his character flaws correctly, he'd start a fight, and would die to the obviously overwhelming power of the fighter. But, I play by the rules. The player won.
So, I had the city watch after him for killing someone in the middle of the street. I figured all the guards were around 3rd level and I believe he was 1st. So, I had him surrounded with 5 guards and a level 5 captain. The player then proceeded to kill all of them, singlehandedly. Then the player asked for his xp for killing them all. figuring he could get to 2nd or 3rd level by this point. I told him that the town would send larger and larger forces against him. He didn't care, he was confident he could beat them, especially after the power increase he got from picking up the items off the corpses of the people he already killed. He pointed out that everyone I sent against him that didn't actually kill him would only increase his wealth, experience, and give him whichever magic items they decided to try to use against him.
I decided to end the game at that point, conceding to his point: Trading a role playing disadvantage for a combat advantage isn't balance. This is why I will no longer sacrifice balance for story reasons.
This process has been repeated with 5 players feeling useless in another game because one player was too good and they felt there wasn't even a point in them showing up to the table. To me, the ability to have a fun combat without any player feeling left out or the combat being mostly pointless because the result is inevitable. That's why I leave most low CR encounters out of my high level games, even if it makes sense story wise because it isn't fun for the players or DM to run an encounter they don't care about.