If a patient is admitted to the hospital, and he leaves without being even checked "the line is too long I'll come in tomorrow". And his condition gets worse during the night - he or his family can sue the hospital for malpractice and win.
From the second a patient is admitted into a hospital - the hospital staff is responsible for his well being.
All the signing is required to protect the well-meaning doctors from being sued vy the grieving family.
It is so much easier to blame the doctor for the death of a loved one - after all doctors can be sued and be legally blamed. Blaming microbs is so much harder.