While I believe that balance is of critical importance, one thing to keep in mind is that balance isn't just about the system; the GM plays a very big role in balance themselves.
Sometimes you have to look at created character and just say, "The balance on this is broken." If the character is overpowered, you may have to talk to the player about changing some of their choices so that they're a little less perfect. If the character is underpowered, you can talk to the player about how to improve their character, or let them play that way if they're having fun and it's not detrimental to the group.
I realize that there are a lot of people who will scream bloody murder at the idea of forcing a player to take suboptimal choices for the sake of the game, but I will point out in a preemptive response that if one person is obviously more powerful, there are most likely others at the table who are losing some or all of their enjoyment of the game because of this.
One of the places where GM as balance really kicks in is when there are a lot of options. Some flavors of D&D gained so many supplemental books that it became easy to find broken and cheesy combinations. In a recent Mutants & Masterminds game I ran (which is point buy), one of the players was just significantly better at building a character than any of the others and chose purely optimal and mutually-supporting powers. He agreed not to do certain things with his character, such as adding teleportation, because it simply made his character unstoppable and it would have ruined the fun for everybody else. (Or would have simply eliminated the combat from the game.)