Ever since I started playing D&D, there's been this huge list of weapons and armor of all types, and very few reasons to choose any option other than "the best". In AD&D, the only reason not to wear full plate came down to cost/availability/weight allowance/ability to use it.
With weapons, it was even worse, because while there were occasional reasons to use, say, a mace instead of a sword, the game itself was written to encourage everyone to be a sword user, if at all possible. And from there, you were encouraged to be a "long sword" user, as it was arbitrarily decided to be the king of weapons.
Even if you liked the 2d4 weapon damage from the broadsword, or the 3d6 vs. large-sized damage of a two-handed sword, if the DM was using the random item tables, you were going to find more long swords than anything else.
And non-swords were generally limited to +3 weapons, where swords could be +5 and had some of the best abilities. 2e's weapon proficiency rules made this even worse, as your ability to use a random weapon you just picked up could mean sucking up a large attack penalty for up to 4 levels!
History lesson out of the way, there are only a few viable solutions to this mess, and each has a potential problem:
1) all weapons of a given type do the same damage. All two-handed martial weapons do 2d6, all one-handed martial do 1d8. Or, for people who want to use 1d12 weapons, like Barbarians, all two-handers do 1d12.
2) a system that arbitrarily has weapons cost "points", so that higher damage competes with cool features. We see this with reach weapons currently; there's no 2d6 reach weapon, because reach is an advantage, so reach weapons do 1d10. So any weapon with a cool feature will do less damage, ala 3e. The problem here is that players who prefer raw damage output will feel upset finding a one-handed martial weapon that does d6 but has three cool specials, and players that hate "boring" weapons will be annoyed when the DM says "look, see? a magical long sword, isn't that great?".
3) a system that binds the damage weapons deal to one's class, so that classes intended to do heavy melee damage do just that, no matter if they are using a rusty spoon or a six-fingered sword made by the finest swordsmith in Spain. Problem here? Multiclassing, players and DM's who feel this is "artificial" and ruins their sense of verisimilitude.
Bottom line is, there is no universal answer that makes everyone happy, and that means that the weapons table must either be so generic that it doesn't matter what you swing in combat, or everyone will gravitate towards weapons that do what they want them to do, and feel ripped off if the reality of the game world says they must occasionally accept a downgrade or sidegrade.
Ultimately, the DM has to solve this for their table, I don't think the game should try to do it for them. If you want players who can feel free to specialize in their weapon of choice, you have to find ways to support this (either by allowing them to have the weapon they want forged, or using some kind of inherent bonus system so it doesn't matter what you're carrying around). If you want players who are willing to use the best available weapon, you need to tell them to not bother poring over the weapon lists or come to your game with any expectations of being a specialist, no matter how "cool" you think wielding dual scimitars would be- sorry Mr. Salvatore, but the idea of a guy using the same two scimitars since 1988 in a D&D game is simply ridiculous, especially when he gets both lifetime blades in the span of the first two books.
