This is true, but the interaction between the doctor and the nurse was invaluable. The context of those orders and the nurse's knowledge of the patient were used to come up with a plan together. Reducing that interaction to "order giver" and "order taker" greatly reduces the quality of patient care. I was recently in the hospital for a week and this was an issue several times.
That asynchronous behaviour happened in the paper world too. Make chart entries, send paper orders to pharmacy/lab, flag it for the other care providers.