One of the major problems with how unarmed combat is handled is that real humans (and we can't possibly know how "real elves" or "real dwarves" or "real dragons" would be) are intrinsically designed to understand how to use their natural weapons (punching and kicking, specifically) as opposed to learning to use weapons (tools). Modern humans have learned to adapt better to using tools, so it stands to reason that modern humans would probably be at least as adept at using weapons as their bare fists.
Anyone knows how to throw a punch. It doesn't take special training or knowledge to punch someone. Knowledge of the specifics on how to punch (or kick) well is another thing, but requires no more training than using a sword well, or using a polearm well.
The problem with a fighter in 3E is that the fighter automatically knows how to swing a sword, or an axe, or a polearm better than he knows how to punch someone. If you try to make a fighter as good at punching, kicking, or wrestling, you are making your character worse overall in combat (in terms of the opportunity cost in taking other feats).
What happens as you learn martial arts, or boxing, or wrestling, is that you learn how to fight. It involves proper balance, posture, and learning to adapt to the change in your opponent's stances, using the distance between you and your opponent to your advantage, using an opportunity in a break in your foe's defenses, etc.
Systems other than D&D 3E have figured out how to deal with "basic combat" and not pigeonhole how you fight. M&M, for example, allows you to purchase BAB and BDB, demonstrating that your character knows how to fight, irrespective of what weapon you choose to employ in a given situation. The Weapon Groups option in UA sort of demonstrates the flexibility in learning to use a variety of different weapons apart from what are forced upon you by the system. If you added grappling and unarmed to that list of possibilities, that might be closer to what I'm looking for.
What I'd like to see in 4E is a fighter who knows how to fight regardless of what weapon he uses. If he specializes in a weapon (or unarmed, wrestling, etc), he's better at using that weapon/fighting style/whatever, but not worse than the baseline in any other weapon/fighting style/whatever.