I agree that the weapons were designed with a specific purpose in mind, but the versatility of the pistol rendered each of those weapons less effective or desirable in those roles. That comes as a result of limiting players to 2 weapons. The Plasma Rifle, for example, might be rated a 10/10 in a specific battle scenario, but a 4/10 in every other. The pistol is an 8/10 in EVERY battle situation, and in a game that limits players to two weapons, who's gonna opt for the vulnerability that those other, specialized weapons provide? Nobody did. So every match was a pistol-sniping contest surrounding the RL and Sniper spawns.
I'm sure you would pick up the shotgun, rocket launcher or sniper. But I doubt the pistol would be the weapon you drop for them (if you still had ammo for it). And if you did drop the pistol for the PR, and you went up against a pistol, how confident would you feel. And if you killed him, would you pick up his pistol to replace your PR? Id vote yes.
There are always the exceptions to the rule, but generally speaking, if one weapon is used far and away more than any other weapon, then its pretty likely to be unbalanced. The Pistol most certainly was. The purpose for a bunch of different weapons are two fold: to ensure that every role on the battle-field is covered, and to afford options for players that prefer different tactics and gamestyles. Mid-range head-shotting should not be the only way to excel at Halo.
If thats the case, why not take out all the maps and put everyone on one, large, flat, untextured square. It would ensure that NOTHING would get in the way of that 1v1 headshotting skill set. It would also be incredibly predictable and boring.