You can always buy equipment to time shift shows and squeeze an extra 3-5 minutes an hour out, allowing you to start at :07 or :07:30. Also, not all networks require the inventory to be run adjacent to the cast. I have always wondered about CBS, because, last I checked, the TOH cost is 4 minutes... I forget if there is a cutaway at :03.
I personally prefer to have a local cast at the top of the hour. jh is right; go all local during whatever hours you are paying someone, and go all national (maybe with a pre-recorded 1 minute local headline cast) after hours. This way, you can start your local cast whenever you want; in some major markets, it's at :57:50 or :58:50, going all the way to :06 or later. If your local news guy isn't good enough to rip some national copy from ABC's, CNN's, CBS' website, and download an actuality or two, why is he working for you?
Dave Ramsey and a number of other hosts start at :06:30; all WW1 news/talk shows start at :06:40. Also, I have wondered about the BOH casts, but I think because the bigger networks run them at odd times (Fox is :30:30, CBS and ABC are :31), local stations just say screw it. Some of the 3rd tier ones just run spots and don't have any news. I say this because it seems those stations running CNN, which does have a cast exactly at :30, usually run the BOH cast.