A skilled painter isn't just someone who is good at applying paint the way he wants, similarly as how a skilled writer isn't just someone who writes the words he intends to write. The skill includes all aspects required to make great pieces.
In the end there is just paint/words. The question how to find and apply the right/wanted paint/words involves many aspects. By training one aspect it doesn't improve the other, but it may or may not improve the overall outcome.