I can usually cite statistics but not on this one. It is my impression from watching 19 Amazing Races that the most common start time is in the morning in whatever time zone the start is. That allows some tasks in that metro area, then a trek to the international airport they are departing from, then a flight out from about 2pm on. Morning in the other 3 time zones is always well before evening in the western time zone.
Prophet, I cannot recall an Amazing Race ever starting in the evening. Please tell me which races did start in the evening. I am talking about Phil's "Travel Safe. Go." and the ensuing mad scramble to vehicles.