Removing the appearance of favoritism at work
Whenever a manager repeatedly assigns undesirable (or desirable) tasks to the same people, it tends to get noticed, even when there's no actual favoritism involved. A visible, random selection process removes that ambiguity entirely — the whole team can see the roster and watch the pick happen.
This works for anything from deciding who covers an on-call shift, to picking who presents at the next all-hands, to running an internal employee-appreciation raffle — the mechanism is the same either way.