Okay, here is a good reason for being on the inside:
The throw from the catcher is ideally received in front of the base, where the tag is applied to the runner, who is usually on the outfield side of the play. A properly positioned 2nd base umpire sees a)the fielder catch the throw and b)the tag of the runner, without having to look through the runner to do so.
Back in the "old" days, the umpires waved safe like a football referee signals an incomplete pass, by crossing the arms back and forth. They signaled "out" by extending their thumbs from their fists. Would you like to return to those mechanics too?
