In this video, Danny Markovitch of Marbin Music makes a case for not tapping your foot when playing with others. I know I’ve had directors and producers both make a similar case (although with the producers it was more about the work required to nix the tapping sound).
A point Danny makes that I really liked, and that I intend to try to internalize and incorporate in my playing, is that we should still be moving around as we play, but those movements should be circular, rather than the false precision of up and down linear motion.