The rationale that I infer is that when people sit down to "write", they enter "writing mode". Writing mode is laden with dogmatic baggage. But the ultimate goal is to communicate, not perform ritual. And since people communicate successfully all the time through speech, it makes sense to suggest that when people write, they don't enter writing mode. Instead, enter "speaking mode" and simply transcribe their speech.
Yes, but. Much speech is filled with hedge words, convoluted phrases, and I'm-still-not-sure-what-point-I-am-making discourse. That stuff needs to go.
There's a fair amount of writing that comes across as if it were literally transcribed from an off-the-cuff spoken exposition, and it is distracting.
In casual speaking it's OK to say, "At this point in time", or, "Let me explain", or, "due to the fact", but if you're taking the time to write you can take the time cut the filler as well.
I much prefer a conversational tone in writing but it works best with some careful editing.