Hmm... Well, my only real worry is things getting overpowered (game breaking, etc). If the Initiators simply "overshadow" the other fighters, then I wouldn't ban the other fighters from a game - however, I would make sure that players knew this before they started playing. I'd say, "Hey, just so you know, if you decide to pick a Barbarian, you might be overshadowed a bit in combat by the other guy playing the Warblade."
From what I'm reading, this really may or may not be true, depending on how they both build their characters, even if it is more likely than not. But as long as the Barbarian knows the Warblade might outshine him a bit, and he picks that class knowing full well what that means, I wouldn't have a problem with them playing side-by-side.
In the end, it'd just be player's choice. I just don't want anything that's game breaking brought into the campaign...
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EDIT: It'd be kind of like a player in a non-Bo9S game deciding to play a straight Swashbuckler. Well... so it's not a very powerful class. In fact, it pretty much sucks mid-to-high levels. But, hey, if that's his choice, that's his choice. And if he's fine with that choice, more power to him. (I, personally, love Swashbucklers - even though I KNOW they are at a severe disadvantage next to most every other fighter counterpart. I just like them!) That doesn't mean you ban fighters because they overshadow a different kind of fighter. You just make players aware of what they're doing, and let them decide if they're alright with it or not.