I really detest the 'barbarian' class, because it carries so much baggage now that it just doesn't need. The class has gone from representing a generic primitive warrior in 1e (which was narrow enough), to in 3e as 'rage' became more and more the defining trait only really representing just that slice of primitive warriors occupied by Norse berserkers, perhaps Judean Nazarenes, perhaps Maori warriors, and a few other warrior cults.
The core concept though of a warrior that garners his strength more from or as much from willpower or bloodlust than skill of arms is much more broadly applicable, and includes - as Dandu rightly points out - examples from what we'd consider the 'civilized' cultures. The archetype here of the raging near psychotic fighter as well a members of primitive warrior cults, covers everything from elite royal bodyguards, elite assault troops, actual psychotics, to religious fanatics. Quite arguably, whether we are talking western knightly tradition or Japanese samurai, multi-classing between the 'skill at arms' tradition and the 'screaming and striking off the other guys head' ought to be a fairly common thing.
And the reverse implication, that all 'primitive' warriors (or even all primitive peoples) are 'barbarians' and basically equivalent to norse beserkers is really no better. Indeed, the implication that just because your living in a nomadic tribal society that you are chaotic, or that just because your society is technological advanced that you are lawful, might even be worse. There is no reason why the leader of a barbarian horde shouldn't be both a barbarian and lawful in inclination, with a code of ethos, a respect for his peoples law and heritage, and a sense that he is part of something larger than himself. There is no reason why a tribe of people, regardless of technology level, should see the individual as being more important than the tribe itself, or be without ethical scruples, or be moral relativists. If anything, isolated tribal bands might be less individualistic and more steeped in tradition and ritual than more prosperous and cosmopolitan societies.
So, I guess I think the whole question is basically wrong. The real question ought to be, "Why do the rules make being a fanatic (barbarian) and being a knight (cavalier) contradictory?", or perhaps, "Why should a barbarian be caring all this unnecessary cultural baggage, that we continually have to ignore when we want to use the class to represent equivalent archetypes?"
That being said, in 1e you are talking hybridizing two of the most powerful classes in the game, with the almost certain result of making a rules monstrosity freed even from its role-playing restrictions.