Hand-written prescriptions can, at times, cause trouble. People want to get their medicine so they can get home and take care of themselves and their families, but if a doctor's handwriting isn't clear enough, the pharmacy can't fill the prescription until the doctor has been contacted. Since doctor's offices are generally closed on weekends, this could potentially keep someone from getting their medicine for two or three days, in some cases.
By requiring doctors to type their prescriptions, we can make things much more convenient for the patients. It's a small, easy thing to do.