The bard, and (of course) the wizard have means to do this outside of combat easily. The fighter has no such means, even though he really should be the leader of men (or at least have the potential).
Yeah, well, there's a strong argument that Conan's a big old Mary Sue, so maybe expecting a game that's supposed to have some niche protection built into it to perfectly represent him with a single class is not reasonable.
Or, maybe Conan's got some bard levels in there.
More importantly - any character could try to talk others into revolting with him. The Bard will probably be better at it, as he's probably put more points into his Charisma and relevant skills, but a fighter should most certainly have a chance.
If that's not sufficient, each character has a chance of getting his or her way by using his or her shtick. Last I checked, the class name was "fighter", not "shmoozer", and his shtick involves fighting. Funny thing, that.