As seen in this article (though not primarily about linguistics), it promptly states:
Some neuroscientists are not so sure. They think that giving up handwriting will affect how future generations learn to read. “Drawing each letter by hand substantially improves subsequent recognition,” Gentaz explains.
Drawing each letter by hand improves our grasp of the alphabet because we really have a “body memory”, Gentaz adds. “Some people have difficulty reading again after a stroke. To help them remember the alphabet again, we ask them to trace the letters with their finger. Often it works, the gesture restoring the memory.”
To shorten the above, writing can help people read and interpret the text faster, which is important in mastering any language. This also means writing words down will also help store these new words into our brains a lot faster. For those with difficulty, people were told to trace the letters and the memories were immediately restored, proof of the effectiveness of writing.
In this other article, the written summary is:
Writing by hand strengthens the learning process. When typing on a keyboard, this process may be impaired. Neurophysiologists have examined research which goes a long way in confirming the significance of these differences. When writing by hand, our brain receives feedback from our motor actions, together with the sensation of touching a pencil and paper. These kinds of feedback is significantly different from those we receive when touching and typing on a keyboard.
Basically, our actions used to write send feedback back to the brain, which is allows the brain to take in information faster, rather than the poor feedback sent from a keyboard.
When writing by hand, the movements involved leave a motor memory in the sensorimotor part of the brain, which helps us recognise letters. This implies a connection between reading and writing, and suggests that the sensorimotor system plays a role in the process of visual recognition during reading, Mangen explains.
And here, writing can also help with reading letters faster and word recognition speed. Visual recognition is critical in learning (and for reading) and writing helps improve these skills.