Understanding the reason why many stations went on 24 hours a day helps know why many do it now but, also, why it´s not a necessity or obligation.
In a few markets, being on overnight back in the 50's was useful but, of course, produced no revenue. The main reason to be on was to be sure the transmitter was on at 6AM. All of us who had a call that went "Boss, the transmitter won't go on" learned it was better to stay on.
As FCC rules relaxed in the 60's, we were able to be on without an operator at the transmitter or even a First Ticket at the remote control point. So staying on the air was a safety measure. Now, with automation, we can do it with nobody there!
Most of those 24 hour businesses make enough money to cover costs. 24 hour radio stations, except a handful, don't bill at all.
In radio's "Golden Age" of the 30's and 40's, few stations ran 24 hours a day, despite there being no competition. It did not hurt the medium.