You have each brought up very good points.
As a CR Level IV Clinician and a Balimo Clinician, I feel it is imperative that all un-mounted exerciss be directly related to riding in whatever discipline you do including English and Western recreational riding. To me this is the only way riders understand their importance.
Every Clinician or instructor has a different background and so will approach teaching a little differently - including the un-mounted work.
Sally's CR Books are wonderful and an excellent add-on to good instruction. Like all written text, we read and understand the information based on our own experiences and missinturpetation happens easily. The advantage of working with an experienced CR or Balimo Instructor is that they can see if you've understood what was said and say it in a different way so it is easier for you to get the right feelings.
Yes, in both CR and Balimo we do use some Tai Chi exercises - really they're Chi Quong exercises - which can be done standing or even on the horse! We also do a wide variety of other awareness exercises to help riders develop Kinesthetic awareness in their own body. This is very important in order for us to be intuitve riders - able to automatically correct the horse before he is out of balance as well being able to more clearly communicate with our horse.
Sally talked about comparable parts of horse and rider - if the rider is tight or blocked in 1 area, the horse will also have a problem in the same area. Balimo works on unblocking the rider through exercises tailored for that individual. The exercises are done mounted or un-mounted depending on the area of the rider that is blocked. For me as a CR instructor, Balimo is the science behind CR. The 2 work best together.
For our horses to be and stay sound, we must ride in balance and be able to flow with the horse's movement. Most front end unsoundness is rider caused. Is it not better to spend your money on good instruction and clinics instead of potential vet bills due to lameness?
Good riding is about both horse and rider having fun and working in harmony together!