When my 9yo was 6-7, she wrote a long story about unicorns, in print letters. She worked on it a little bit every day for several weeks, if not months. Then she stopped, and haven't showed any interest until very recently. The ideas that I hear all the time, would be writing lists, writing notes to each other, writing letters, and so on. DD was never interested in any of it.
I think for her the issue was perfectionism. She wanted the process of writing to become more fluent. The whole penmanship journey started when she was 8, it was a long one for us, and lasted for months. She wanted to, but wouldn't practice. She would reject my suggestions, and wouldn't come up with her own, and yet she was upset about not being able to write.
I showed her dozens of fonts, bought half a dozen of various work books, until she finally found a style that she liked. Then she practiced--still very little, and wasn't impressed with the lack of immediate results. Eventually she wanted me to make up a handwriting game for her, and after a few false starts, she finally was into what I created. It was related to horse breeds, involved some magic, some geography, and very little writing. Then seemingly all of a sudden (well, it did seem that way ) her handwring was lovely, and she was writing. Still, not much. But she wrote a letter, many notes, and many opening paragraphs to her stories, but she is not inspired or motivated to work further on them right now.
I also modelled writing to her, by writing to do lists and posting them on the wall each day. I do this anyway, but I made them visible to her so she could see the process and the need for them. She is not very into lists, but she did see me writing.
So from my perspective, if she's writing a word, that's plenty.
My DS (6.5) writes when he draws comics, it is a much more natural and organic process for him. He is very good at copying, so he can copy any font / style he sees, and at times comes up with very mature handwriting, but when he writes on his own, it is all uneven print. He is so engaged with his art, crafts, drawing, that I don't worry about encouraging him to write--it seems like it will come, when the need arises. DD has never been so engaged, and she is often lost or 'bored', so I tend to over suggest to her and over worry about her skills.