That was the question posed recently on a forum I frequent.
I would respond that writing is not engaging the same areas of the brain that are used for reading and pattern recognition in general. We may be mixing the ideas of writing to improve character recognition and writing to improve language in general as well.
So we have to ask, writing a word X times has value towards improvement in what? If the goal is to improve pattern recognition or recognition of characters, then it seems to me that if a kinesthetic element is desirable to engage more parts of the brain, the kinesthetic element should be focused on a recognizable sub-part of the character — whatever “key” it is that makes that learner recognize the character. And the kinesthetics do not necessarily have to correspond to the motion of writing it in part or in full. The desire is only to engage more of the brain.
Writing characters over and over does seem to work with what’s popularly called “muscle memory”, which you can see with the phenomenon of being able to write the whole character once you get past stroke # whatever — that the writing task becomes automatic when you get started. But then how will that help modern users of Chinese if the primary input medium for real compositional writing in Chinese is the computer (unless a handwriting input tablet is being used?) So I would guess that repeated writing of characters really only benefits what I like to call mechanical writing skills (remembering how to form the characters) rather than compositional writing skills (being able to put the right words in the right order to make a text).
In terms of improving language overall, the same principle of engaging more of the brain holds true, but it’s desirable to incorporate some semantic and tonal information into a kinesthetic element since the intention is to reinforce not only the written form of the character but also its meaning and its pronunciation (and probably to encounter it in the form of a word, not a single character, and to encounter that combination in the context of a text, and to have that text have personal meaning to the learner would be best).
I’ve heard as well that engagement of the limbic system (emotions) has also been shown to improve retention, so maybe what we need is a way to get really excited about characters? 😉
Writing Chinese is so time-intensive an undertaking that for me it goes against common sense to imagine that one could not move, say, three times the character forms into long-term memory by using methods specifically aimed at the particular desired outcome (recognition) in the same time it takes to do so by writing them over and over (even with spaced repetition as mentioned above). I would use mnemonics, gestures, and contextualized practice (scaffolded reading, for example) in combination with individual items (like flashcards of words, not single characters) to drive reading skills in Chinese.