Tony Vargas -
What I was trying to say with "Mechanics are absolutely not arbitrary" is that mechanics shape how we understand the game and its world. If the magic system, for example, is similar to Call of Cthulhu or like the Conan RPG, where spells are hard to get, difficult/risky/painful to use, and ritualistic, then players have very different understandings of what place magic users have in the world than a system more like D&D, where there's a magical economy, spells are just as easy to cast as swinging a sword and have no drawbacks, and instantly and immediately useful.
Similarly, if the way that the melee class works is that you can do one thing - swing a sword - that resolves the same way every time, players respond by getting the idea that warriors are ordinary, unintelligent, and mundane. However, if melee combat works more like 7th Sea, then players respond by getting the idea that swordsmen are dynamic, crafty, flexible, and Dramatic with a capital D.
In the same way, the relative similarity or difference of mechanics between classes changes the way that players think about those classes. Historically, melee classes and spellcasters were mechanically quite different and perceived that way, to the extent that many people felt the degree of separation in 4e didn't really reflect their understanding of what the two groups were. I don't necessarily agree that they were right, but I do see that there's a continuum of perception when it comes to mechanical differences.
So...if all melee classes use the ED mechanic, is what's left sufficient to make the classes feel different? At the moment, I'd say no for the Fighter - the Fighter's shtick right now is the ED mechanic and the Fighting Styles are basically just lists of ED maneuvers. If the Ranger, Barbarian, Monk, Warlord, and Rogue all have ED dice and maneuvers, I don't think there's enough there atm to give the Fighter a unique feel. To use an analogy, if ED = spells, then the Fighter doesn't have the equivalent of the Sorcerer's Willpower and Sorcerous Powers or the Warlock's Boons and Invocations.
Ainamacar -
I said "Why should there be connections, if they don't exist in the class concepts?" So the question is, to what extent are there connections. Adventuringness isn't it, because Wizards are adventurers too, and they are quite distinct from Fighters. I would also add that "principally focused" isn't specific enough to be a good connection - a War Priest is pretty damn focused on physical weapons, but interacts with them through spells that allow them to attack and do spell effects at the same time.
Like I said, the way they interact with weapons is profoundly different. A Fighter has undergone formal, martial training; a Rogue or Ranger or Barbarian hasn't. They have done other things with their lives and don't have "the common language of martial interactions." Warlords are close enough that I'd say some form of dice make sense - they've gone through similar training to the Fighter, with the difference that their training has revolved around how to manage and direct Fighters on the battlefield rather than their individual fighting style.
As for my Paladin example, I'm going off of the
Paladin design goals, which emphasize very different themes. "1. The paladin is a champion of a divine calling...2. The paladin can see and smite evil...4. A paladin has divine abilities." To the extent that Paladins are described as warriors, they are described thusly:
3. A paladin is a fearless and selfless warrior.
The paladin is a warrior, nearly as skilled as a fighter and typically armed with heavy armor and a sword, and utterly without fear. When a paladin fights, it is not only to impose his or her code on the unworthy and slay threats to his or her divine calling, but also to protect allies. More so than the fighter, a paladin who champions a good deity or moral alignment is willing (and able) to sacrifice his or her own safety to ensure the safety of his or her companions. To this end, a paladin aspires to find a blessed sword of unequaled power: a holy avenger.
Now, to me, I see this quote as emphasizing that Paladins are going to have similar proficiencies and attack bonuses to Fighters, but they are going to play differently to Fighters, perhaps through some mechanic that lets them take on the damage that their allies receive.
Overall, I just think ED would overly clutter the Paladin class. Keep in mind, this is a class that already has sense evil, smite evil, lay on hands, turn undead, cast a limited number of divine spells, and call a mount.