I grew up watching the BBC, and even though I emigrated from the UK before the famed "I ask you again minister, is that a yes or a no" repeats of jeremy paxman, this was something that always struck me about politicians on the BBC: why did they keep coming back?
What I've realized over time was they kept coming back because they had to. If you were a UK politician at least well into the 1990s (and arguably right up to today), both the media infrastructure and the social culture required your appearance, even if you knew that David Marr or Paxman or whoever was going to chew you out.
That's not true anymore in the USA (it may also not be true in the UK either). There's really no reason why anyone needs to appear anywhere. Get a reputation as a fiery take-no-bullshit interviewer, and you won't be doing any interviews.
I don't think there's any way out of this now. The media landscape has exploded, and there's no outlet that is of enough importance anymore to hold people's feet to the fire.