I don't really see a compelling reason to split the fighter into a host of different classes. I can see differentiating it from the rangers and rogues, who use knowledge about their environment as major aspects of combat, but a fighter can easily be built, primarily, as highly skilled in all basic forms of combat, with options to specialize in types of combat, which are best used with - but not exclusive to - certain weapons.
The quickest, dirtiest way to simulate this, at least using 4E concepts, is to give fighters every kind of weapon expertise rider ability for free at level 1.
Ignoring the to-hit feat tax thing, this gives fighters the following abilities when using types of weapons:
Axe: When rolling damage for a weapon attack you make with an axe, you can reroll one damage die that results in a 1, but you must use the second result.
Hammer or Mace: You gain a +1 feat bonus to the number of squares you push or slide creatures with weapon attacks you make with a hammer or a mace.
Bow: You gain a +1/tier bonus to the damage roll of any weapon attack you make with a bow against a single creature that is not adjacent to any other creature.
Crossbow: You ignore partial cover and superior cover with weapon attacks you make with a crossbow.
Flail: When you hit with a melee weapon attack using a flail and the attack lets you slide the target, you can knock the target prone instead of sliding it.
Heavy Blade: While wielding a heavy blade, you gain a +2 bonus to all defenses against opportunity attacks.
Light Blade: You gain a +1/tier bonus to the damage rolls of weapon attacks that you make with a light blade against a creature granting combat advantage to you.
Polearm: While you hold a two-handed polearm in both hands, you gain a +2 bonus to all defenses against charge attacks.
Sling: When you make a ranged or an area attack with a sling, you don’t provoke opportunity attacks for doing so.
Spear: When charging, you gain a +1/tier bonus to damage rolls of weapon attacks that you make with a spear.
Staff: When you make a melee weapon attack with a staff, the weapon’s reach for that attack increases by 1.
Any: You can use a minor action to sheathe a weapon and then draw a weapon.
Put all of that on one character, and you have someone who can use any weapon at any time with a bit of oomph. Other characters can still get just as much oomph, but they have to pay for each weapon they can do so with. The character is suddenly able to switch weapons in combat to match the situation, and can make use of different weapons for different tasks, but no weapon is useless for any task.
A fighter with a two-handed sword can still push, just not as well as with a hammer. A fighter with a bow can still fire point blank, just not as well as with a sling. So on and so forth.
The problem that fighters have faced is that all of their abilities get tied into using one specific weapon. If they lost that weapon, they became a joke until they found it or replaced it. This is true in 4E as much as any other edition, unless you use inherent bonuses. A fighter should never lose half of their abilities and most of their damage because they've had to borrow an axe while they retrieve their sword. Remove this issue, and you can suddenly spend a lot more time giving them ABILITIES that weapons ENHANCE rather than putting all that effort into making weapons into their own builds.
