A scenario to consider which I don't think has come up so far:
Engine shutdown in a 2 or more engined A/C or pilot incapacitation with no further complications in either case and pilot issues MAYDAY.
1 minute after MAYDAY issue another A/C in the vicinity reports uncontainable flight deck fire and wishes to divert to same airport. A/C 1 as I understand it has priority as it issued MAYDAY first, unless maybe ATC negotiates a downgrade to PAN (which would take time at the very least).
Wouldn't want to be a PAX or crew in that 2nd A/C the day this happens.