Similarly, flights also don't seem to be scheduled to arrive at exactly midnight either, even though there's no risk of passengers showing up on the wrong day in that case.
True, but that's replaced by the risk of those coming to greet them at the airport showing up on the wrong day.
I think avoiding date ambiguity is probably the main reason why flights are not scheduled for 00:00 departures.
For flights departing past midnight, I always make a point to state 'flight leaves at xx:xx, night of <day-1>, early morning of <day>.