Have you noticed how many good speakers are also writers? Doesn't it seem that many of the greatest speeches were given with few or no notes. Was there no formal preparation? Was the speaking was extemporaneous?
No. There was written preparation by great speakers for great speeches. Additionally, there was a body of writing done by the speaker that helped them build their ideas and formed the foundation for speaking.
Consider Winston Churchill - an inspiring speaker and author with a large body of work. Martin Luther King Jr. - he left behind voluminous writings both public and private. Abraham Lincoln - an Attorney, the schooling for and practice of consists largely of writing.
Look around, you'll find the people that are the best speakers have a background in writing, a habit of writing. I know many lawyers. I've seen lawyers trained and seen the changes that training causes. Lawyers write, a lot. It's a key element of their schooling and their practice. When they speak, it's well organized and purposeful. They learned by rote, through practice - writing.
In short, this had led me to the conclusion that I need to write more.