The problem is that even if the fighter is all of these he's still the most useless class in the game because he can't DO anything besides hit stuff with a hunk of metal. He can't move obstacles out of the way, he can't talk his way around a fancy dress party, he can't stop a demon from carrying a princess back through a hellish portal.
Giving the fighter more plus signs isn't the answer. He needs effect buttons, he needs something on his character sheet that allows him to tell the DM "now this happens" instead of begging for the DM to come up with rules for him to swing from chandeliers on the spot.
I beg to differ. The Essentials' Slayer is awesomeness personified. A slayer doesn't have to be built to be a wielder of two-handed weapons. Several of the stances that a slayer uses don't specify whether an attack must be melee or ranged. So "poised assault" would give a +1 bonus to an attack using a longbow. Choose the "bow expertise" feat and add another +1. The "mobile blade" stance would allow our archer to move up to his DEX modifier each time he hits an enemy. That's a lot of motion (move-attack[hit]-move again; next turn: move-attack[hit]-move again). Since the slayer adds his DEX modifier to damage, then the archer-slayer can pump up his DEX to 20 and thereby cause massive amounts of damage with his bow-and-arrow (d10+10) at level 1.
Now, it's true that there are only two weapon specializations: the Greataxe and the Greatsword, and the slayer misses out by focusing on weapons other than those two. It's a shame they didn't expand the slayer's weapon choices (maybe they did; I'm not a subscriber to DDI).
But the slayer, if he is trained in healing, can make a dying companion automatically heal and stand up. He has some "controller" abilities, forciing enemies to shift around. He can shake off certain effects, like being slowed or immobilized. And he has more options to increase his mobility during battle. He does more than just hit things with a sword. The slayer is very much in the mold of the classic hero-warrior.
The knight is the more pure "defender". With his defensive aura and features that give him benefits when using a shield. Like the slayer, the knight has options that allow him to heal his allies or move his enemies around. The choices of which skills to train become important to both slayer and knight, because certain powers require training in particular skills. I point this out because of the comment that fighters need other skills to deal with out-of-combat situations. Well, a knight with training in Diplomacy not only has the ability to persuade the duke to give his party aid, he also has the ability to reposition his allies in combat, based on his Diplomatic training (if he chooses the appropriate power).
The powers these classes have do not, in my opinion, feel like "anime magic". There are no "daily powers", though there are encounter powers. Both fighters make basic weapon attacks, and use their powers to augment their attacks.