Smilin Ed
Outside the USA, the home of private enterprise, a lot of airports are indeed privately-owned.
Even in the USA, it would appear that public owners do not invariably squander taxpayers' money by staying open all night when there are no operations scheduled.
Do you have any notion of the cost of keeping all those people there "just in case"?
There will always be somewhere reasonably close that is open, ie a major city airport.
Looking at airports in West Virginia, for example,
KMRB Attendance: MAY-SEPT 0700-2100, OCT-APR 0700-1900
KCRW Attendance: CONTINUOUS
KHLG Attendance: MON-FRI 0700-2300, ALL SAT-SUN 0800-2000
Now, you can argue that of those only Charleston is used regularly by airlines, and you would be right (I think). But the others are publicly-owned, and have runways that are lit (as far as I can see) and quite long; they have navaids, and would be useful in a real emergency to comeone who has nowhere else to go. What they may not have is a CFR service at the right category, but that doesn't seem to worry you.
Lesbos isn't that big either, and there are plenty of airports open 24/7 reasonably close by.
If you seriously believe that every public airfield should be open 24/7, I suggest you take up your crusade with the FAA. When the USA does it, I'm sure the rest of the world will follow.