I shoot manual with Auto ISO and AI Servo with the focusing area set to center zone. The zone focusing solved a lot of problems associated with center point only focusing, like a rapidly-moving main subject moving off the center point or two main subjects separated by a space in the center, resulting in a perfectly focused background and a fuzzy main subject.
When you refer to zone focusing - which mode exactly are you referring to? There is one called Zone AF and then there are Expand AF Area or Expand AF Area: Surround.
I sometimes will shoot with zone focusing, not the expanded feature. If basketball players are charging towards me for the basket, and I'm along the wall behind the basket, zone helps because as the player goes up for the layup and defenders are there, I cannot determine which part of that scene is going to be closest to me. If zone is selected, the camera will automagically pick the correct point on the scene to focus and if aperture is narrow enough, everybody is in focus. I rarely us expanded point, but that would be useful if you were tracking the basketball and it got slightly away from you. Zone covers more ground.
As far as using the 5D Mark III for sports, I have to be able to. I doubt at tennis and golf matches anyone is going to want to hear the shutter firing on my 1D X