Definitely the main issue with late arrivals is having sufficient staff available. In 2018 I was on a very late running flight from Skiathios to SOU. With such a late departure, it was obvious that there could potentially be problems, although nothing was mentioned form the flight deck or from cabin crew before departure. About half an hour into the flight the captain broke the news that Southampton would be closed and we would be diverted to Exeter, not the easiest place to travel back from in the middle of the night. The cabin crew were marvellous, spending much of the flight going up and down the cabin trying to find out where people were trying to get home to so taxis could be arranged and where possible, doubling-up small groups going to locations that were close together. Just after passing Paris, the flight deck informed us that Southampton had agreed to stay open - so all was well and we landed at about 23.45.
What many people probably forget is the shear number of people needed to keep the airport open. Fire crew, control tower, apron staff, ground handling/baggage, border control, baggage reclaim, long-stay car park bus driver etc.
It relies on goodwill and the overtime bill must have been a considerable cost, but there again, so would the coaches and taxis!