Children like to write. Sometimes the problem is getting them to write on a piece of paper, instead of on the wall or some other off the wall place.
What age should a child begin to learn to write? It would be nice if the answer to this question had to do with neural development, hand coordination, and such well studied answers. The real answer is much more practical: children must learn to write when they are being given written assignments as part of their education. Something as simple as a math practice sheet or a written test requires that the child have an ability to wield a pencil somewhat accurately.
As children grow, their fine motor control improves. That is an intellectual way of saying what you already know: younger children cannot write as well as older children. Younger children require greater spaces between the lines in order to form their letters and numbers. One can expect better formed letters from older students. See the Vanguard Writing Practice Pages for recommended line spacing, based on the student's age. This web page also includes free handwriting practice sheets you can download.