I know - but had Garrosh gotten the upper hand legitimately, would he have pulled that finishing blow? Of course not, because Cairne's accomplishments and benefits to the Horde be damned, he insulted Garrosh's honor.
My point is that no leader in the Alliance would behave that way. The closest we have to internal conflict right now is the dwarf-chick, and I don't see her insisting on any duels to the death anytime soon.