I've often wondered about this as well, I'd imagine the art department. Handwriting always looks annoyingly 'perfect' in movies and I don't mind this for period pieces when educated people wrote aesthetically pleasing and with attention to form.
There is a similar annoyance I have in the horror genre when they show pictures that children drew that show the 'monster' or evil; in most cases these do not look like something a child would draw, but more likely a design artist.
P.S. one of my favorites, "The Dark Half", has a brilliant sequence where the main character is linked telepathically to his 'dark half' and receives communication via writing! I'd need to check but I believe it is Timothy Hutton himself who does the actual writing, maybe not for the closeups but the clip below has an establishing shot where it focuses in on his writing prior to what they show.
Handwriting is an art. I bet a calligraphy artist is employed. Trust me, the average graphic designer (in the art department) doesn't necessarily have good hand writing skills.
In my films I hired a friend who was a wonderful artist who actually was near sighted. I myself had one of the best handwriting you will ever see, but I passed the job to my friend and others. Matter of fact thinking about it now. I should have taken that talent further. A few of my bosses recommended over the years I should have. But there are so many different things to do and roads to take in life.So be it