Kinda ironic that your comment is a good example of this style, in describing your feelings using an “I” statement without attacking the speaker.

If it were limited to "when you do blah, I feel blah" verbiage, it would feel like that. But it's more generally about taking accountability for one's own side, while listening to the other side, without needless escalation. I can't really see a flaw with that approach, other than it taking more work.

I wonder how many arguments would be defused if both sides could phrase the other side's point of view in a way they would agree was accurately stated.

Really? I do a similar thing when dealing with idiots (not idiots, fully formed human beings, with a legitimate point of view, probably not evil, probably quite normal in person) on the internet.

I find it helps keep me sane.