In the following excerpt, from a TED talk by the Korean writer, Young-ha Kim, switch the word "writing" for drawing and there one indisputable explanation for importance of gestures.
"...The reason I make them write like crazy is because when you write slowly and lots of thoughts cross your mind, the artistic devil creeps in. This devil will tell you hundreds of reasons why you can't write: "People will laugh at you. This is not good writing! What kind of sentence is this? Look at your handwriting!" It will say a lot of things. You have to run fast so the devil can't catch up..."