If you rename the Warblade the fighter you are pretty much just trading 3rd for fourth, since that's what 4th did for all the classes.
Fighters are iconic because they are the master of the feat, which means they're pretty much a blank class for you to customize for any combat style you choose. The Wizard does this with Spell Selection.
Clerics are a pretty specific class, but it's one you see in pretty much any Rpg out there in some form. Rogue as well to a lesser extent, if your Rpg has any kind of atmosphere they'll be there.
Those are the big four, so WOTC had a duty to do right by them.
Bard's really just a different flavoring for rogue, or a hybrid between the utility of a rogue and that of a wizard.
Sorcerer is exactly what it appears, an alternative to Wizard for arcane spells.
Paladin and Barbarian are pretty much prestige classes in base class form.
Druids and rangers are, as many have argued, different flavors of the same class.
These were added in because they were popular, asked for, and patched up holes in character options. Plus they let players jump more quickly into roles they commonly wanted to play without contriviance.
Monk's pretty solidly original though. Probably why they mesh so well with psionic settings, moreso even than without. Warlocks are a lot like monks, except on the opposite side of the coin. I would have included something like the Warlock in the base classes, except with a little more balance to make the Warlock less rampagingly strong. And this is coming from someone who adores cheese.
Beside that I'd probably swap the Rogue out for the Bard, and rename the class. If you want a minifighter customize your Fighter. And play Halfling.
I'd probably merge the Ranger and Druid and find a happy medium, while emphasizing their incredible versatility being balanced by their focus on being versatile, you know, outside. Paladin and Barbarian get to be prestige classes again, though probably the easiest ones of all time to get into.
The only thing I don't know what to do with is the Sorcerer. An alternative to the Wizard is too obvious to throw out but they're thematically identical. the only option would be to make them more different. Perhaps different ways of casting spells.
All that said, if we were just focused on supplementing the class list instead of tidying it up, I'd have to go with Warlock as a big first candidate, rebalanced of course. Dragon Shamans are mechanically unique as well, though thematically they clash a little with Warlocks. So either them or Marshalls. Other than that everything else pretty much branches off the big four.