First, author recommends challenging but feasible deadlines, not "arbitrary" deadlines.
Second, the "small increments" approach you describe is quite compatible with the approach of having workers give a status update every Friday. Requires determining what can be accomplished in a week, so you have something tangible to report on Friday.
Yeah, one man’s "challenging but feasible" becomes the next man’s "arbitrary".
The difference between small increments and giving a status updates every week is that if your task needs multiple status updates, it’s not small increments.
Also small increments mean a piece of work that can measurably be evaluated as done. A status update is not a "done" status.
If someone fails to deliver a small increment, you find out soon, and the team can re-assess, and it doesn’t carry the stigma of missing a deadline.
Second, the "small increments" approach you describe is quite compatible with the approach of having workers give a status update every Friday. Requires determining what can be accomplished in a week, so you have something tangible to report on Friday.