Re: Charlie Watts
He's self-taught so it's probably something he stumbled on in the early days and it's still the most natural way for him to play. Maybe when he started off he didn't have the coordination? Or maybe it was easier for him to accent the 1-a and 3-a upbeats to get the beat bouncing? Maybe he liked the clean snare sound? I've never heard or read an explanation from him.
Self-taught players tend to have quirks about their playing. A lot of them are handicaps but every now and then someone like Charlie makes it work.