Agree with JackSprat's mom...I think SH's idea is to be able to use (this) exercise to create an honest response, not just 'hope' the horse is relaxed (in the walk or work desired). So using leg yield is an access point to check in that the horse honestly "allows" you to use your aids- not aggressively or in a worried way as he says but in an easy way...here in the walk. The walk will then become relaxed and rhythmic through the horse's acceptance of the rider's (leg yield) aid.
IF the horse is being worked for relaxation then it must remain in the walk until it is relaxed there. It's rather like doing flying changes, get it and then walk...and walk until relaxation is sustained (10 strides or 10 minutes). Doing endless transitions where the horse is not (allowed) telescoping/oscillating/swinging in the back is contradictory to mental/physical relaxation.
LY is suppling, not engaging.
But isn't that just the "wait and hope" ride? If your horse is jigging for nine minutes do you just let that go on and on without comment or do you riderect and ask for access? Hey horse, come on, let me ride. Just passengering for ten minutes doesn't do much, and then when you are in a tense situation, where is your "come on, let me ride" button? Horse says yeah yeah, maybe I'll let you when the clinic is half over.
The transition was engaging, the LY was suppling to encourage relaxation and gain access to the horse.
I agree with whoever else said the saddle looked awfully bouncy. Perhaps a properly fitting saddle would relax the horse too instead of BOUNCE BOUNCE BOUNCE all the time.