I once saw Bob Costas bragging that he does his own stunts including the tongue-twisters. He then very impressively gave an example of a lengthy, complicated and convoluted string of words and effortlessly continued to introduce the next segment of his show. I wondered if multiple takes were required. I would guess that he was able to do it in a single take. Some people are good at that sort of thing.
I have been on Radio and TV a few times and I've had to make presentations in front of large classes and audiences. I find that if you stumble and make a mistake, the natural tendency is to dwell on it internally even as your mouth has already moved onto the next sentence. While you try to contemplate the error, react to it, or learn from it, your mouth has already moved on and you find it very difficult to concentrate on the task at hand.
Sometimes when you're humming along nicely and everything is going smoothly you might start to think about an important point that you are about to make. Internally you are already planning out the next segment but out of your mouth is flowing the segment at hand. You will likely have trouble with it.
Those who are best at this sort of thing will be the people who can block out both the past and the future as they move in the present.
Tripped up by the words that came before and those to follow.
I talk today, not yesterday, not tomorrow.