Just to get a ballpark idea of the force involved in a quick stop in Sport mode:
If the MP decelerates from 17.8 m/s (40 mph) in 0.75 seconds, that's 23.73 m/s**2, or about 2.5 Gs. I don't know if the assumed stopping time is correct, but it's probably in the ballpark. Since all of the force needed to stop the MP comes from the rotors at the ends of the arms, it would be roughly equivalent to supporting your MP only at the ends of the arms and loading about 4 pounds on the body of the drone. (This is only the deceleration force provided by the rotors, and does not include the mass of the MP itself.)
Is this momentary force, applied repeatedly over time, enough to damage the drone's hinges? I don't know. Some Phantoms had shell cracking problems around the motors, including some Phantoms that were claimed to have never been crashed or landed hard. Maybe hard stops were a contributor?
It's something to think about if you're in the habit of hitting Pause or just snapping the right stick back to center while the MP is at high speed. Maybe they are designed to take it; I don't know. If a hinge fails in flight during a hard stop, though, the bird is definitely going to fall.
Not trying to tell anyone how to fly, just sharing some thoughts. I like Sport mode too.