Do we really know that, though? I was just joking with Greg, but does a spot on the bridge, be it at helm, science, engineering or communications really mean you're qualified to take command of the ship?
While Uhura (for example only) may have rank and time served over Chekov, does she have the training or even the experience to command the ship in an emergency situation? IIRC, and guys who have served can correct me, if Chekov is placed in command by Kirk, he's pretty much in command even if Uhura out ranks him. To be in command you have to be in the chain of command. If, as a comm officer, Uhura is outside that chain her rank as irrelevant as McCoy's.