Well seeing how I work in the "Real Sports" world, I'll just say this. There is no AF for professional sports video cameras. It's all done manually. I have friends that operate those large, 17X lens, sports cameras and can keep a baseball in focus all the way out of the park.
I was shooting stills of my son's basketball game tonight and at one point I turned the camera back to horizontal and shot a few minutes of video. I was using my super cheesy, but highly effective jar opener focus lever on my 24-70L from the baseline. I had no other supports or apparatus to shoot video. It didn't turn out too bad other than I was too busy messing with the camera to seriously watch and follow the game properly.
Overall, I think that maybe you could actually shoot sports with these cameras with the right set-up, but there are so many other better options to do this. I was shooting stills at ISO 2000 and kept it there to shoot the video so maybe it wasn't all that great, but even with the basic focus puller, I was able to keep things pretty well in focus and that was with no rig, monopod or any other support. I was also shooting at f2.8. So if you had lets say a youth soccer game on a sunny, Saturday morning you could easily shoot it at f11 or smaller and have some super deep DoF.
With a rig, my basketball effort could have looked a lot better. But I wasn't there to shoot video. So I switched it back to still mode and laid it over to shoot in vertical orientation and kept shooting stills.
Yeah, my son's team won the game pretty handily.