Well, we stay stationary or pretty much so - takes too much energy to chase horses around, especially when you've got several that have to be worked. So I don't think you'd call us Monty Roberts type trainers at all. :)
Some horses we are working in a 40ft or 60ft round pen, you can use a line there - some get put in the 100ft pen - no line. 'Course if they don't behave, they go to a smaller one with a line.
Our horses are all trained so that we can put them on a line (say at the show or an endurance ride) and lift a hand to lunge them - sometimes just voice commands because there we don't have a ring to work them in and they need some settling of nerves and stretching legs after a long trailer ride. And there it's critical that they behave and obey without any correction equipment because it's important since we always have horses for sell that people see that. Am I making sense here?
You betcha. Makes perfect sense. I like, and think there is a place for liberty training, and the versatility of knowing both.