I've always enjoyed this topic. I've not always enjoyed the broadcasts. As I mentioned earlier, these shows are built for high cume, and repeat stories, (especially weather and traffic) at a horrific rate. If you watch any early morning newscast longer than 20 minutes, you will start to see repeats.
That being said, most big markets (from my informal internet search), run 4:30 to 7 am. Fox, of course, has no network obligations in the morning, so they run wild through 7-9 AM. Fox also tends to make their morning shows more entertainment than news. Not in all cases, but many.
I look at these hours as prime real estate for most local tv stations. There are no viable alternatives, so why not increase the visibility of the brand. It certainly can't hurt, and the overhead is usually low.
Of course, there is a direct correlation between the morning start time and the length of commute in each metro. This is why, in general, smaller markets don't do the 4:30 start. In my market, which is around 300K, most start at 6 am, not 4:30.