Has a doctor ever written a drug prescription or other things on a piece of paper maybe after examining you?

If they have, you should by now know what I'm saying.

Why are doctors handwriting terrible and so difficult to decipher the meaning of what they have penned down?

If you were to see 30 clients a day and recommend handwritten prescriptions to every one your penmanship would degrade too.

Also, they've a form of medical shorthand they use that only the doctors and pharmacists understand. Have you ever heard the pharmacist complain when deciphering prescriptions? I know I haven't.

You make it sound as if doctors are taught atrocious handwriting in med school..
Anyways, it's not the case for all doctors. There are doctors with neat and legible handwriting.
Those with chicken scrawl handwriting don't actually have bad handwriting (not all), they just chose to write that way so as to save time and attend to other patients....
What do you expect of a man with a vast number of patients waiting for examination?
You can try comparing your handwriting when you are in a rush/ under stress and when you are in a relaxed state. You'll see the huge difference

An average Nigerian doctor sees over fifty (did I exaggerate?) patients in a day. Now, if you were a doctor, would you have the time and patience to design an award winning prescription note for your fifty-something patients everyday?