The answer: College radio station does must have morning programming if someone is willing to do it.
There's no FCC rule that a radio station has to sign on at a certain time of day. However, 20 or 30 years ago, I think college radio was more popular than today. I know my old station used to be on the air from 7am to 2am everyday.
Sometimes the program director had to ASK for volunteers for some morning shifts, especially weekends and during the summer. But he'd find them. Today, that same college station signs on and off at random, depending on whether somebody wants to do a given shift.
It's funny. The sign off was recorded years ago, so it ends with "Good Night." These days, the sign off is often played in the middle of the day, even though the voice still wishes us a good night.