Yes, I agree, typically songs used begin in the overnight hours, however, many of the stations now are so familiar with the artists and their songs, that they have changed this. Many stations know what songs are going to be hits right out of the starting gates (Justin Timberlake's "Sexy Back", RBD's "Tu Amor") that they premiere them with the largest audience to get them familiar with the song, then play it frequently throughout the week. Afterwards, they play it based on listener reactions.
RBD's "Tu Amor" premiered on KIIS-FM's "On Air with Ryan Seacrest". Clear Channel knew that it would be a hit in LA since their audience was familiar with the group, so they premiered it with a large audience.
Yes, it is a gamble in some sense, however, take a look at the songs premiered on the morning shows, and find one that really hasn't been a hit. Their system usually pays off.