One wonders how much this is a function of the soundbite culture of US television news? If one only has 16 seconds of footage, it is rather hard to show all the setup, leaving it easy for communications directors to pick what gets covered. The Reagan team elevated this to an art form.
I’d also note that C-SPAN typically does a good job with their coverage of media events, since they cover the whole thing live. There, you get a very good sense of the entire atmosphere.