I wonder too! MY DD1 is a 4th year med student (so qualifies next year) and we have joked that her handwriting and spelling might be the death of some unfortunate patient...we hope there is a good pharmacist who can read and spellcheck!!!
However, there are realtively few exam papers of that sort.. medical training is a complicated mix of coursework, exams that are basically tick the box (but you have to know hell of a lot to make the right selection) and what might be called practicals... Just as well!
I'm married to a consultant and in my experience their handwriting gets worse the longer they are in the job. His writing was bad at uni but just about legible it's now officially worse than our 5yo DSs.