I know how it sounds. I know. But, as a riding instructor I can speak from the experience of having genuinely seen it work in every client of mine that has tried it.
As I've written about on many occasions, having an independent seat is vital for good riding. Common problem areas are tension in the hips/pelvis, stiffening of the back, and stiffness of the arms or shoulders. If you are stiff, tight, or restricted in any of these areas, it will almost certainly impact how you ride; your balance, the refined communication with your horse, and your horse's ability to carry you well.
One of my favourite (albeit newer) techniques to improve tension areas is to "breath into" that area. Some people find it really easy, and it comes quite naturally for them, for others it takes work. As a rider myself, the thing I struggle with the most is actaully remembering to do it!
Many, many riders focus on the head and neck when schooling. At Elementary levels upwards, a greater element of collection is needed, but a lot of riders forget that their is an entire horse to collect. Their version of "collection", not that it really is that at all, comes from bringing the head and neck up and in. Meanwhile, the back end trails out behind the horse, who hollows their back and drops onto the forehand.
Horse can't bend? Shoulder-in. Horse not bringing the inside hind under? Shoulder-in. Horse heavy on the outside shoulder? Shoulder-in. Pulling in transitions instead of pushing? Ride them in shoulder-in. Needs the wall for balance? Shoulder-in. Not enough expression or suspension in the paces? Shoulder-in.
I am a dressage trainer and general equestrian coach in Surrey, Sussex, and Berkshire. I teach dressage lessons, and hold a range of riding and equestrian clinics around the UK, and use my blog to share horse training tips, advice, and resources.