I wonder if OSS and focusing compete for the processor. If so, turning off OSS might improve focus tracking on fast moving subjects. But if OSS and focus don’t compete there may be no advantage to turning off OSS. The situation may vary with manufacturer or model.
Since Sony only recommends turning OSS off for tripod use, perhaps there is no advantage to turning it off for any other situation. I don’t like to speculate, so I‘d like to think of an easy DIY experiment that would answer the question for my particular model.
Maybe it takes time to move the sensor around as well as the lens focusing element or whatever is adjusted in the lens to counter the movement of the rig. With a SS over 1/500s, the movements aren't finished.
Also just speculation.