The LBBs have this to say about weapon use by class:
"All magical weaponry is usable by fighters.... The whole plethora of enchanted items lies at the magic-users beck and call, save the arms and armor of the fighters (see, however, Elves); Magic-Users may arm themselves with daggers only.... Clerics gain some of the advantages from both of the other two classes... in that they have the use of magic armor and all non-edged magic weapons (no arrows!).... [Elves] gain the benefits of both classes and may use both weaponry and spells."The first three descriptions might refer only to magic weapon use, but the ability of elves to use spells and weaponry, ordinary or magical, makes it clear that Fighters were meant to be unique in their ability to use any weapon. I've mentioned my personal interpretation of what to do with "Gandalf with a sword" before: no HD/attack bonus for Magic-Users except with fists and daggers. But the flip side is that I would give Fighters the HD/attack bonus on any attack, even things like throwing an urn in a barroom brawl or pushing a branch of a tree down to hit a rider in the forest. Anyone can try these things, but only Fighters get a bonus.
Large, heavy stuff thrown, pushed or rammed into enemies does the standard 1d6 damage in the hands of a Fighter, as does a tree limb or bench used as a two-handed improvised club. Again, the benefit of using one weapon over another in a 1d6-damage-only world is what you can do with that weapon: a Fighter armed with sword and shield who meets a rust monster is going to want to improvise a weapon from something non-metallic and preferably long, to keep the monster at bay; a Fighter in a barroom brawl might have a chance of hitting up to three opponents simultaneously with a bench.
Not all improvised weapons do the same kind of damage as a real weapon, though. Some might act like combat tricks, with the "damage" roll being used as a Change Situation roll instead: tearing down and throwing a curtain at an opponent, if successful, wraps and tangles the opponent on a 2 or less. In other cases, the damage can be treated as stun damage unless the roll is high, either treating all 6s as real damage or using the brief system for blows that stun instead of damage. Thus, throwing a playing card as a weapon requires a d20 attack roll; if it fails, it didn't strike, otherwise it did, and there's a 1 in 6 chance of actually doing serious damage, like piercing the target's eye.
I think this safely avoids the "kittens with sharpened claws" proficiency problem, not just because I don't allow proficiencies, but also because it's the temptation of only using what you know your good at, with a limitation on what weapons you can be good at, combined with no distinction between the non-damaging functions of weapons, which produces players who pick a weird proficiency in something that in theory should only be usable once or twice.