No one has yet answered the question how often an airline will deny rebooking based on their assessment that then passenger didn't move fast enough to reach the connecting gate. It is assumed that MCT is met and that all flights are on time. We have had a statement that everything will be ok if the passenger does not dwaddle in shops or lounges on the way. We have not addressed slow walkers, medical issues, etc. or failure to use carts, request wheelchairs (that don't show up), etc. Also while advising to arrange longer than MCT is absolutely valid, that is still not an answer to the OP question.

I think the answer is that they would never deny rebooking short of something completely out of hand such as talking to no one, going to a hotel, and showing up two days later expecting to be put on a flight.

For myself, it has never happened that I have not been rebooked, but it has also never happened that I haven't moved "fast enough." The closest personal experience was a late arrival in DTW, we ran, the flight was buttoned up, they opened the door to the airplane by going down the jetway and pounding on the fuselage behind the cockpit window, that on NW.