It is just manners or ground work training, no reason why they have to do that. I expect a lively horse to trot away then kick, bolt, buck - if they do not, they would be driven away with a lunge whip.
A former horse of mine would bolt with the halter and lead rope, and me for a second attached. Not fun. Then you have to trudge through a field to get the halter and lead rope back once they have stood on the rope and come to a stop.