Some people with beautiful handwriting are not particularly talented at drawing. There is probably a correlation between handwriting and drawing ability – after all, both use the same mechanical apparatus between brain and paper, so people with e.g. poor muscle control will suffer in both uses of those muscles. But it’s possible to separate the two, to have the physical ability to move a pencil precisely, but to only have developed the ability to write well, and not to draw well. If someone only practices writing and not drawing, they will learn to precisely recreate the same 26 shapes without learning how to make an arbitrary image.
Perhaps more surprisingly, it’s possible draw well but still have sloppy, illegible handwriting. That’s surprising because most schools spend so much more time on writing than drawing. But I think this disparity is not due to spending more time practicing drawing than writing, but to a difference in how these individuals’ brains process the actions of drawing and writing.
Though they are superficially similar, for the average person writing and drawing are different activities. The mental experience of writing is more akin to speaking, with arbitrary motions learned by rote and reproduced automatically as we think about the words we intend to write. By contrast, drawing is free-form, producing novel and arbitrary shapes, and our mind is focused on the lines we are laying down, and on the image we are trying to capture with them. For most people, writing is not drawing letters, but speaking in ink.
However, for some people with poor handwriting, I think this distinction may be weakened or absent; rather than repeating a rote process, each letter is created anew to draw the word on the page. Their handwriting will be inconsistent, mis-proportioned, will fail to stay on the line, etc. Their handwriting may be described as “childlike”, and that seems to fit: because they are still learning to shape the letters and coordinate the muscles, their writing process similarly resembles drawing. But for some individuals the distinction never develops, and they continue to draw letters. Additional practice will improve muscle coordination, and as with all drawing practice the writing may become more precise, but it will never reach the automaticity of normal, rote handwriting.
If this is so, we should expect to see a subset of people with bad handwriting who are very inconsistent in the way they form their letters, e.g. not having a fixed order of producing the lines that compose a letter, or changing the purpose of a line after it has been drawn. Because drawing letters is less wrote, it is less prescribed, and the same letter can be produced in multiple ways and often is (people with good handwriting may do this too, but I would predict that where they do it is rule-bound, e.g. a letter is drawn differently depending on the preceding letter, but always drawn the same way under the same conditions).