There are methods of handwriting that allow you to avoid hand cramps. The Palmer method of handwriting, which was popular in America at the turn of the 20th century, emphasized using the whole arm and shoulder to make marks on the page. In order for this method to be effective your wrists must be limp in order for your arms to slide quickly across the page. Instead of consciously "drawing" letters, you build up and use muscle memory to create letters, in the same way you naturally build and use muscle memory when you throw a ball. If you master this method of handwriting, you can write at 60 words per minute, for hours at a time without your hand cramping. Unfortunately, the Palmer Method was abandoned when education reformers in the U.S found it too "difficult", because it requires months of training and practice to become proficient. It also required left-handed students to write with their right hand, because English runs from right to left and this method requires your other hand to manipulate the paper. As a result, generations of Americans have grown up using an inefficient, painful method of writing.

Of course, the manuscript writers needed to draw the letters in a calligraphic style, which necessitated precise wrist motions. So a writing method designed for brisk mark making wouldn't have helped them.

EDIT: I'm not saying that I support forcing left-handed people to write with their right hands. It may be true that the Palmer method (or any right-hand only method) has a history of teachers using corporal punishment to punish mistakes, but corporal punishment is of course not necessary to become proficient.

Eksith, you're right that "drawing" the letters doesn't have anything to do with the speed at which letters are made. The "drawing" comment was made about why many people's cursive handwriting is so poor. When students learn cursive now, too often they are simply copying letters from a book or blackboard ("drawing the letters"), instead of practicing the physical motion. So when students need to write cursive script quickly, they don't have enough time to render each letter correctly and consequently they develop their own methods muscle movements, which usually leads to sloppy handwriting. The same kind of thing can happen when you are taught to type. Correct touch typing teaches you to let your finger return to the home row after pressing a key before you reach for another key. If you aren't taught to do this, you will develop your own muscle movements that are suitable for typing some words, but lead to mistakes in others.

A common error is letting your finger hover near the letter you typed when the same letter is repeated in the word that you are typing. This seems like an "optimization", but it isn't, and causes lots of spelling errors because it can easily mess up your key press timing. Using your own "optimizations" might be able to type as quickly as a touch typist in short stretches, but it is far more likely that you will make more errors.

https://en.wikipedia.org/wiki/Palmer_Method