I have a couple of those, too. I didn't really stress making them show work until algebra, as long as the answers were right, but I did model for them, and also explain the value of communicating your thinking to other mathematicians. Math is a language, and it's good to be able to learn to read and write, as well as speak it. We've also talked about 1) the massive inconvenience of having to re-work an entire multi-step problem in order to find and correct an error, vs being able to check steps that you have already written down, and 2) real-life consequences that ensue from minor calculation errors that could have been prevented by the engineer/scientist/architect/etc. writing down calculations so that errors could more easily be caught. And, incidentally, that some day they may want the partial credit that classroom teachers will award only if they can see your work. One of mine has an interest in teaching, so there is special value in emphasizing the power of mathematical communication.
Some children find their hands to be too slow and awkward to keep up with their thought process, which is why my #2 prefers not to write things down, if it can possibly be avoided. When we did SM primary, I scribed almost everything, down to "four, carry the two", to separate fine motor development from mathematical development.
