For me, the issue with that, is that I'm more of a "stream of consciousness" conversationalist, where I say things as they come to mind and rarely have time to parse them in the way you suggest.
It is; I think a lot of people go for stream of consciousness speaking because they're afraid if they pause someone else will take over the conversation. But the reality is that people's attention span just drops down after a sentence or two, especially if it's stream of consciousness - they have to spend more and more energy to follow your thoughts. Which is absolutely fine in some situations, but it's not the most efficient.
Your message comes across a lot more clearly if you get your thoughts in order before starting to speak. This is difficult at first, because if you're not practiced the conversation will have moved on before you've got your thoughts in line, but it is a skill you can practice. Take one of your stream of consciousness statements, maybe write it down, and repeat it a dozen times, each time making it shorter and more to the point - assertive, definitive, without feeling like you have to expand on your every point. Assume that if something is unclear, the other party will ask. But also try and limit the amount of concepts in one sentence so you don't overwhelm the other party with new stuff. (assuming you're talking technology or something of course).
I find stream of consciousness rambling to be extremely irritating. Normally, I'm very much against interrupting, but I have been known to butt in to stream of consciousness speech, saying, "Okay, and what's your point?"
In my experience, that doesn't help. They don't know what their point is yet; they're just gratuitously holding conversational priority, so they can say what it is the instant they figure it out.
Once I detect stream-of-consciousness, I do a warning signal, like a frown or a yawn, then I make a visual cue that I'm exiting the conversation.
The Church of Interruption and Barker conversational style just doesn't work for me. I expect to be able to speak complete thoughts and listen to complete thoughts--thoughts that have a timely conclusion.
I find this most irritating. It is much more polite to the listener if you do your homework first and then start talking. It vastly increases the chances of being able to capture and hold and audience's attention.
For me, the issue with that, is that I'm more of a "stream of consciousness" conversationalist, where I say things as they come to mind and rarely have time to parse them in the way you suggest.
Maybe it's a matter of practice.