When a doctor's office calls in prescriptions, there are a couple of problems: For one, it takes away time the nurse or office manager could spend doing something else. For another, the likelihood of error increases. Some of these medications sound very similar and it's really easy to mistake one drug or dosage for another. Similarly, faxing over a prescription can generate mistakes or time delays since faxes can fall to the floor or handwritten scripts, especially when faxed, are easily misread.
With e-prescriptions, the doctor, nurse, or manager, simply pushes a button on the computer screen from the EHR, usually, and sends the typewritten script to the pharmacy of the patient's choice. The fact that you're still waiting is more about your pharmacy's policy than the system! Some pharmacies don't fill a script until the patient shows up. I steer clear of that kind of pharmacy, personally!