Honestly, even though focusing on specific weapons has been the fighter's gig from Unearthed Arcana 1e through 4e, I'd like to see it put to bed now.
I'd like a Fighter to be pretty much equally awesome with whatever he happens to find - swords, axes, bows, maces. And heck - still scary with beer steins, ladders, bricks, and coffin lids.
In most D&Ds these days, the rewards of specialization are so great that it's crazy to have a weapon-using character without it. And then, it becomes dumb to use anything other than their single best weapon.
I'd like Next to finally butcher this sacred cow. I don't think it makes the game more fun; I think it rather straight-jackets weapon-using characters. It's a boring way to spend a feat.
EDIT:
In ADnD, usual fighters were specialized in 4 or 5 weapons, and if they found one new, they could specialize in it too after a while...
...sorta.
In AD&D, you had to become Proficient in a limited number of weapons and you were varying degrees of bad with everything else, depending on your class. Options to Specialize didn't come around until Unearthed Arcana, but it was a welcome addition. Specialization in 1e is pretty beefy - it gives you more attacks, sorely-needed bonuses to hit, and extra damage. You could also double-specialize, which was pretty insane. I forget the rules on multiple specializations - I want to say it was restricted, but can't remember atm because it was frequently houseruled one way or the other. Even so, you'd still be hauling around another weapon for a few levels.
In 2e, the idea of "group" proficiencies came about, and it was an improvement over the system. But I really think the whole Weapon Proficiency system was a weak point of the two editions.
-O