I agree about the knight and the gladiator, to me they are both more like backgrounds, or knight becomes a title that has to be earned through game play (that's another issue).
I totally agree about the knight. I think the fighter subclass should be called the "defender" and the knight should once again be a background. Knighthood is a title. It's a social thing, and it shouldn't be limited to just fighters. There's no good reason why a paladin can't be a knight, or even a wizard. Sir Elton John is a knight in real life, and he's a bard.
I'm pretty sure that when mediaevel people talked about "knights" they didn't have in mind Sir Elton John and his ilk; the idea of knighthood as a pure honorific is more modern. The standard referent of "knight", as used by a mediavel person, is mounted, heavily armoured warrior who is also a noble (the two statuses track one another, because only nobles have the resources to equip and train themselves in the requisite fashion). Given this, I think it's harmless enough that D&D has fighters as knights, but not wizards or rogues - they might be nobles, but they're not knights - they don't ride horses in heavy armour charging with lances.
That paladins, and certain sorts of clerics, can't be knights is a different issue. But that doesn't so much show us that knight should be a background rather than a sub-class, as reinforce the broader issues currently being debated around what exactly makes for a distinct class. In 4e, for instance, if you want to play a heavily-armoured melee warrior you can be a fighter, a warlord, a paladin, a battlemind, a runepriest or a cleric. Any of those could be used to build a knight PC.
Within the current design paramaters of D&Dnext, the solution might be a
cavalier sub-class for the paladin and a
templar sub-class for the cleric.
As for gladiators, besides fighter the other obvious candidate would be a rogue. Maybe a "street scrapper" sub-class might do the job.
If you really want to strip away all aspects that are more background then you might even have to examine thief and assassin. Both of those are things any class could conceivable do. A fighter who steals or kills for a living could be either of the two.
I don't think a fighter should be able to be played as an assassin, though. A fighter should be designed to play as a frontline combatant - relying on good hit points, good defences and reliable damage output to win fights. Whereas a mechancially viable assassin needs to be capable of spike damage from stealth, but therefore requires (as a balance trade off) a certain squishiness if events move from stealth to fighting out in the open. In D&D terms, that is a rogue build, not a fighter build.
For instance a samurai, a wugen, a ninja all should be backgrounds not subclasses. A samurai might be a fighter/warrior, a wugen might be a wizard/warlock, a ninja might be a rogue/assassin. So separation of game world from subclass, yes. Separation of background from game world impossible.
The same point applies - a fighter or paladin can't be a ninja. A ninja is a form of assassin.
To the extent that a wizard
can be a capable assassin or ninja, this shows us something about the wizard build - it is really a form of magic-using sneak/skill guy, and hence should be designed having more regard to how it sits with, and doesn't make redundant, the rogue.