I don't think that melee weapons in FPS games are terribly overpowered, because of the old "knife to a gunfight" adage. Melee attacks are deadlier in games these days to make them actually worthwhile. If you had a melee weapon or attack, that had the same strength or a lower strength than a ranged attack, why would you ever bother with it? Melee attacks in games require a proper use of strategy, stealth, and timing to pull off well (obvious exception for me is Halo, where you basically just go in swinging). If a player gets sloppy trying to beat everyone to death, he'll quickly find out why FPS stands for first person shooter.
Also, some one of the more recent games I've played had a great balancing factor for melee combat. In Left 4 Dead 2, melee weapons were added in to the game, allowing you to unleash the pain up close. All of the weapons do basically the same amount of damage and are all basically the same weapon (I think the frying pan has better hit detection, and the Kitana can decapitate multiple enemies at once, but those are small things). Also, the Chainsaw is a nasty piece of work, shredding any enemy in a few hits maximum. However, now players have a fatigue system in place when using melee combat, to ensure that they can't just keep swinging away without being impeded. After you swing about 5 times consecutively, you can't swing until the fatigue recharges. This can leave you in trouble in the middle of a horde, or while trying to fend off a tank. Also while the chainsaw is incredibly powerful, it has a long rev-up time, meaning that you have to anticipate a horde. However, it's all worth it to use the ultimate zombie-killing chainsaw technique, THE SPINNING DEATH BLOSSOM...OF DEATH!!!