In therapy riding, the reason they want close contact is because they need the "rider" to feel the horse's movement....the forward and back movement of the hips of the horse mimmick how a person walks and this gives the "rider" therapy, this makes their body move normally as if they were walking and therefore stimulates those muscles that they don't use regularly (if they're in a wheelchair, they're not walking, so being horseback bareback, their body is made to move as if they were walking). Also, as it was said...they get sidewalkers to hold em up.
That said, bareback will be good for balance only if you do it right. What I mean is, there are people who ride bareback, but they balance themselves with the reins, hold the reins tight, pulling on the horse's mouth (not meaning to but it happens) and they clamp their legs around the horse. This isn't going to teach you how to ride properly. It'll only cause you to have bad habits for riding in general, and when you get a saddle, you won't have the balance you need.
To ride correctly, you use your SEAT to balance and keep you on the horse's back. your butt is your seatbelt. that's why real cowboys have little butts.:wink:
You don't want to use your lower legs, but your upper thigh (not your knees) and your butt...you roll your hips forward and back (squeezing and releasing your butt cheeks) with the rhythm of the horse's movement....speeding it up (not exaggerated) with the horse at a trot and going with at the lope. Bareback will help you really feel the horse (but you can learn to feel in the saddle, too....but yeah, bareback, obviously, there's more instant feel)
The better you learn to loosen up your hips, and roll with the horse's movement, you'll learn overall balance for when you ride in the saddle or bareback.
You can learn to post bareback and really strengthen your thighs and butt even more for great overall balance. Again, as long as you don't use the reins or your lower legs or knees to grip/balance which happens easily when bareback riding.
If you need to grab the horse...then grab mane. Also, when bareback, use a pad (no stirrups!) it's easier on the horse's back if you do.
So...yeah, bareback riding is a good way to go for overall balance and learning to ride well. I did it early on and it taught me a lot. I was learning how to ride, and used a dead broke horse that was stout and it was in a small enclosed area when I started.
If you've never ever ridden before,...you can go bareback but be aware of the falling off factor. You can be lead around on a well broke horse by someone at a walk for a few rides, and be on a longer line and gradually be left on your own (with someone teaching you without them holding a line, that is)..... They do the same in riding lessons with saddles, ...the teacher leads or lunges the student.
Also,....you can pretend to be bareback on a saddle by simply not using the stirrups.