Whatever. Again, All of this can be quickly dealt with by application of common sense.
Right, but IMHO, the JOB of the designer is to apply common sense to the rules. The DM has enough to deal with without having to re-write the rules, too.
Now your getting it! Weapons operate on two principles; the point and the plane (although a better description is 'they strike precisely to put the hard end through the bad guy). All weapons operate by manipulating the weight/energy through two points (yes, they do exist in your one hand). From there you apply edged,point, or blunt force trauma. Mechanically, using the hammer IS the same as using the axe. the proficiency isn't in wielding a longsword, it's placing the slashing damage where it's most effective.
Okay, why have different weapons? Why have different weapon proficiencies? If you're advocating simplification and abstraction to that degree, why bother with different statistics for the weapons?
Given these factors, why is a halfling fighter trained in these principles going to have a hard time appling them to a slightly different weapon (or any trained fighter, for that matter)?
In reality, a person who knows fencing is going ot have a hard time applying the same principles to a spear or throwing a punch or getting in a knife-fight. The weapon rules emulate this reality by using different weapon proficiencies: unarmed strike, rapier, and dagger are all seperate weapons. Real life gets even more grainy than this, in that someone who knows a fencing rapier will need more training before they can know how to use a real one. Someone who knows how to punch a man won't nessecarily know how to use a glaive, even though it's all the same kind of motion.
The game rules, which want to simplify reality, but value the diverse differenses between punching a man and putting a spear in him, reflect this with different weapons. I value this too, so I think the rules make the game better. If you don't value this, why accept even the 3.0 weapon rules?
Anyway, a trained halfling fighter doesn't have any problem applying these to a similar weapon. But a dagger and a longsword are no more similar weapons than a fist and a rapier. In other words, it would be an oversimiplification that I wouldn't enjoy in the game.
Maybe you would, and that's fine, but certainly that means that the 3.0 rules were off for you, too, and that the 3.5 rules moved the game farther from that abstraction to a more concrete representation of the differences between weapons. That may be a problem for you, but certainly you can understand that people like the aspect of the game that shows the difference between an axe and a sword just like they like the apsect of the game that shows the difference between a druid and a cleric, or a sorcerer and a wizard.
Thing is, gaining this insight takes years, which is why only fighters can wield all simple and martial weapons. They didn't spend the same amount of time with each weapon. They learned the larger weapons first, then applied those tactics to the smaller blades. Later weapons took less time to master. Heck, most fighters probably have never seen most of the weapons in the PHB, yet they can use them.
Well, that's one interpretation, but it definately doesn't have to be the only.
I'd argue that no, they did spend the same about of time with each weapon. While wizards learned to break the laws of time and space, fighters could certainly educate themselves on the subtle differences between a greatsword and a longsword. This is why they have a higher attack bonus than wizards -- they know the weapons and the difference between them to such an extent that they can use the weapons better to hit enemies better.
The weapons in the PHB are all available in any town with a high enough GP limit, and even the smallest towns have enough GP to accomodate the vast majority of the weapons. So unless you're using DM fiat, no, fighters have seen the vast majority of the weapons in the PHB, and have trained with them, learning the ins and outs of these weapons as they learn the ins and outs of heavy armors and shield use.
The Fighter class, like any other class, represents a lifetime of skill in their first level. The weapons they learn are not just swung around in two different ways, but are tools used for their appropriate tasks. You don't use a longsword for the same thing you use a hammer for. The abstraction that you recommend would equalize the two, and that's a level of abstraction that would remove some of the strategic fun of the game, and some of the verismilitude inherent in the rules.