This is done to save money. There's probably a rack of boxes handling the dirty work. 99% of users of the system are local, as in the same time zone. So if you kill the boxes at night, you save half of your electricity bill with minimal inconvenience.
Obviously you can solve your little dilemma in the cloud by scaling based on demand, but not everything can be put into EC2 or similar. Government sites that handle sensitive data certainly can't.