I agree with your analysis regarding fairness, but it is an oddity in that is one of the few situations where the standard flow of the game (win and you stay on, lose and you go to the end of the rotation) is not followed. So in that sense there is something a little unfair about it.
Also - I know a 3 team playoff to 7 points with double-point scoring would take much too long!!!
Notice I said one of the 'few situations' above because I knew you would come up with the examples of pair-off playoffs where the winner does not stay on for the very next point.
