Draw reins and martingale?

Hey all,
First of all I'm an eventer through and through so this is more out of curiosity than anything. I don't know much about how most people ride/train in the Hunter world.

Anyway, there's a girl at my barn who started riding hunter and has her own coach come in to give her lessons. I've been riding at the same time as her a few times and saw that her coach makes her ride with regular reins, draw reins, and a standing martingale. To me it seems really odd to use draw reins with a standing martingale, and jump with the draw reins on. Usually I only use them to teach a horse how to go in a dressage frame if it isn't quite getting it.

Is it common to work in draw reins and a martingale at the same time? And jump in them? What does this accomplish?

I've never seen both used at the same time before. Jumping in the martingale is common, but jumping in draw-reins is VERY dangerous as the horse can get caught on the slack between their legs. If the rider gets left behind or has a poor release, the effect is amplified if the rider catches the horse in the mouth.

Fairly common to jump with a regular martingale in the hunter world. I'd think using both is highly redundant and I would think they just have the standing on there out of habit more so then necessity. The draw rein thing bothers me 98% of the time. Some people I know feel that it gives them added control when they're jumping. Some people I Know use them to help their horses balance in between the jumps. Someone I know uses it as a technique to help her horse jump better: horses jump well by rounding their body AND lifting their legs. Some horses do one or the other and need help developing the other. This trainer I know uses the draw reins to restrict their horse's body so they're forced to try harder with their legs. Personally I think gymnastics are more effective and safer but... to each their own right? (in her defense she's been doing it for years and her horses all go around healthily and happily and she hasn't had any accidents...yet)