The fact that we have collarbones and horses don't means that, unlike horses, we don't have to breathe in synchrony with the motions of our forelimbs. But just because we don't have to doesn't mean we don't, and observation suggests it may be more natural when we do. Looking at the (mostly women) tennis players who strike the ball with a grunt or squeal suggests that there is something irresistible about emphatic vocalization when an emphatic gesture is being made.
It's the same impulse with marching songs - probably popular in all cultures that are fond of marching; is it a coincidence that narrative verse tends to adopt the same rhythm? Reciting Virgil, for example, one gets through about 10 lines in a minute – 60 feet, that is to say, each of which consists of two parts: what the Greeks originally called the thesis (setting down of the foot) and the arsis (lifting of the foot – during which process, of course, the other foot was being set down). That means 60 double paces a minute, in 2/4 time. That is the rate of march Napoleon prescribed for his armies.
The Old English line reads at about 14 lines a minute – four accents in each line, 56 double paces, in other words, compared with the 55 which was the standard of the British army (maybe French soldiers had shorter legs). Middle English accentual verse is the same – and like Old English verse is readily analysed as following a basic 4/4 time in which most marches are composed.
Chaucer, Milton, though writing in a different convention, also give us verse that reads at about 15 lines a minute and often provides a 4-accented line.