The "official" reason I take time to run a writing center in kindergarten is to give students the opportunity to witness firsthand how writing works. Students come to the circular table and dictate a story. I stretch out their words and write them down, occasionally underlining the Soundabet sounds as they come up. For example, if you click in to get a closer look at Hailey's story, you will see that I underlined /th/ in "with," the /sh/ in "she," and the /ar/ in "part." My intention is that students will see how writing works and then venture to try some writing on their own. If your child begins to write, praise their efforts! And, please, generously overlook spelling errors. It takes courage to write!
A more important reason for having a writing center is to listen closely enough to show I care. Stories of significance sometimes arise in these sessions. Hailey's tale here relates the death of her first hamster, Popcorn. Writing in kindergarten is an occasion for connecting, not simply a dessicated exercise in learning the mechanics of writing.
If you think about it, connecting is the reason to write in the first place.