When we created the current version of OpenLP, one of the things we wanted to do was declutter the interface as much as possible. Having lots of buttons just overwhelms new users and makes it harder to find the button you want. Therefore we tried to put only commonly used items on the interface (I actually think we still have room for improvement, but we had to make some compromises!)
I'm afraid saving the same file over and over with different names isn't something that occurs very often for most users. When it is required, the file->save-as menu suffices.
Also some widescreen laptop screens often don't have much vertical space, so we'd rather devote more space to the service items than to buttons.