Well, we've got several options for the order.
Stage, Winner, Loser (Currently used)
Stage, Loser, Winner
Winner, Loser, Stage
Winner, Stage, Loser
Loser, Stage, Winner
Loser, Winner, Stage
Of those only one is viable.
#2 isn't an option because the winner can character CP the loser.
#3 & 4 are no good because they give the loser a DOUBLE CP.
#5 & 6 have the same problem of letting the winner CP the loser.
If you bring double-blinds into the picture, things can change somewhat.
Picking the stage first then double-blinding basically makes it useless as a CP, since the stage CP is negated by seeing it, and the character CP is gone.
Double blinding characters THEN doing the stage could be worth considering, my only concern is that MK is still broken in that case. People would pick MK no matter what, since if the loser goes MK & the winner DOESN'T, they give em the ****.