I know this because in a previous life I took a course in sociolinguistics, taught by one of the world’s great demolishers of the idea that anyone ever utters anything that actually makes sense. One of the most memorable class activities was to record and then transcribe actual conversation. And then, upping the stakes, to record and then transcribe a formal lecture. I recorded and transcribed a conversation among my friends about a tamagotchi (all the rage at the time), and then a formal lecture by a professor widely regarded as being one of the best lecturers on campus.
When you do this, this is what you learn. People do not talk in complete sentences. They certainly do not talk in paragraphs. People rarely have a point, and almost never build up to that point in any systematic way. A good lecturer (unlike a pleasant conversationalist) will have an overall structure, yes, but actual delivery comes with asides, anecdotes, incomplete sentences and stutters, and ums and buts, and my new enemy, “so, …”.
Graham’s advice should not be to write like you talk, but rather to write like you imagine that you talk. Here is the distinction. You imagine that when you talk, there is structure to what you are saying that can be broken down into a series of component claims that flow naturally from one to the next. You imagine that you use proper grammar and clear language that is just precise enough but never obscurantist. You imagine that you have a point. Imagine if your writing did the same!