I think it helps to watch the video of Thackery saying them outloud at the end of the post. The rhyming gives counting off in groups of five and then 20 a kind of rhythm that "1,2,3.." lacks.
I suspect if you have some sort of monotonous task that involves counting, the rhythm makes it easier to not loose your place or have your mind wander.
I suspect if you have some sort of monotonous task that involves counting, the rhythm makes it easier to not loose your place or have your mind wander.