I'm all for having the base combat/class system being able to support all sorts of different styles without having to have special classes or new rules additions just to get them up to par. However I don't want to make players choose between optimal and cool. There should be a way to get whatever fighting style you want up to par without a huge opportunity cost. I'm a bigger fan of cool that realistic, and I don't want to have people have to jump through a bunch of hoops to do what they think is cool. And on the flip side I don't want everyone feeling like they are obligated to stick to certain weapons (especially if it shouldn't be a common choice) just because they are better.
That would be a good dial to have in the system, the realism <-> coolness dial.
I'm not sure how well it would work though, and I'm not even sure what it would do.
Frex, daggers. Tradiaitonally daggers in D&D are a low damage weapon that is cheap, concealable, easy to use and throwable. If you don't need to throw it or smuggle it or have a wizard swing it, a sword is simple better in every way.
In reality it's more complex. A throat cut by a sword does not make you notably more dead than one cut by a dagger, nor a stabbed torso. The sword has the advantage defensively because of it's greater range. In close combat or a tight press on a field the dagger is superior to the sword. D&D captures none of this and has never tried to. I'm not even sure it should try.
Suppose I want to make a dual whip wielding character because it looks cool in my head. Should the system forbid it? No. Do I deserve special rewards for being creative and special? No. Or rather, you already got it when the system allowed you to portray the character you wanted to. You do not get to whine and mope however when MinMax does more damage than you dual-wielding axes. Axes hurt more than whips. That should not change just because they look cooler in your head.
Really if you want to make all weapons balanced you just remove the distinctions between them.
Suppose instead of damage based on weapons, you had damage based on class + level. So a fighter is always more dangerous in melee even if he has a dagger and the wizard has a greatsword. Then you can assign a few properties to weapons that give them situational bonuses or open up a maneuver.
So a weapon table might look like:
Dagger: Melee, Close Quarters, Throwable
Long Sword: Melee, Standard, Skilled
Spear: Melee, Long, Braceable/Throwable (choose one)
Mace: Melee, Standard, Armour Piercing
Club: Melee, Standard
Whip: Melee, Long, Flexible
Longbow: Ranged, Fast, Skilled
Crossbow: Ranged, Slow, Armour Piercing
Really, there is a lot of merit to a system like that, where you might give rangers a bump in ranged damage but not melee and vice/versa for fighters.
But I don't think it would fly. Even 4e didn't go that far, despite keying damage to class + level in the powers system they made sure to have differing weapon damages in the system.