Balance is the #1 most important skill for a rider.
How can a rider help the horse to achieve balance if the rider themselves cannot find balance?
I see riders every day, Training Level all the way to Grand Prix, who rely on their legs to grip for balance, knee rolls to hold the thighs down, or the reins to keep from falling back in the saddle. Finding balance on an animal that is moving is not easy and can be a constant struggle. However, if the rider cannot ride without holding onto the reins for balance, it will be nearly impossible to create true self-carriage in the horse and will cause problem areas in the horse's body. If the rider cannot relax and trust their body, the horse will always hold tension in the neck and back, and will have difficulties moving freely.
I spent over a year working on my position on a lunge line. My instructor, Carolyn Rose, made me ride without stirrups at all times, to allow me to find my balance without relying on any external devices. I encourage everyone, of all ages and skill levels, to take periodic lunge line lessons. Having the horse controlled by a ground person allows the rider to focus on their body and position and to feel the horse's movements through the seat.
A great example of this method is the Spanish Riding School in Vienna, Austria. The instructors there keep the riders on the lunge line for months to help each rider develop an independent seat. Many riders associate the lunge line with "lesser" beginner riders. Considering that the totality of the sport of dressage is about balance, why would it only behoove a beginner rider to focus on this foundation? Why would it be seen as "below" the rider to learn the bio-mechanics of themselves and their partner?
The rider can also develop balance through riding the horse bareback, without the saddle. This should not be done too often, as the direct pressure to the horse's spine is not beneficial for the horse. It is informative to feel the horse's back muscles without the obstruction of the saddle, as the rider can better understand how the horse moves and how their own body affects that movement. Feeling the energy move through the horse's top-line is an incredible experience.
Here is a video of me riding Gryphon, a Friesian gelding that I had in training in Florida. In the video I demonstrate riding bareback at the walk, trot, and canter.