The posture and position of the rider is probably the most important factor in how well a horse is able to use itself. However achieving the 'correct' position is an art in itself if the rider is not to feel stiff, or uncomfortable.
Here are few reasons why the rider needs to consider their position:
If the leg and foot are in front of the rider then it can result in a braced knee and ankle and the seat pushed to the back of the saddle. It may well feel quite comfortable and secure for the rider, but it will cause problems in the trot and the horse will have too much pressure on the back and probably through the reins - even if the rider doesn't feel that they have too much contact.
Legs and feet too far back will result in the rider tipping forward and dropping their weight onto the horses forehand, can cause tripping, stumbling and the rider will feel a little precarious at times.
Slumped or rounded shoulders and head forward and down will cause unsteadiness in the hand and horse tipping onto forehand.
But, adopting shoulders back heels down etc etc approach will just cause stiffness and tension in the rider and cause other difficulties for the horse. Good position comes ultimately from the independence of the seat. This means that the rider can balance perfectly without reins or stirrups, and without gripping when the horse is walking, trotting, cantering or jumping. Once a rider can be balanced in this way then the 'classical' position happens all on its own.