It’s easy to ‘read’ a rhythm, metre or tempo when it’s shown in body movements (e.g. swinging, knee-bends, side-to-side movements of the torso or head and so on). To indicate the type of music you want by using rhythmic movement, rather than (or together with) words or counts is a very effective way of communicating tempo and pulse and metre.
I’ve often wondered why it seems such an arduous task to mark an exercise in tempo, but then I wonder whether it’s because the kind of movements that really help to convey a sense of rhythm are precisely the ones that you’re not supposed to do at the barre – a bit like trying to eat a doughnut without licking your lips.