Elkin. The King Who Could Not Sleep

The King Who Could Not Sleep is a children's book by Benjamin Elkin, with art by Victoria Chess, published in 1975. It is available at the Internet Archive.

Here is a YouTube read-along:

I'll admit I was not happy with Benjamin Elkin's failure to acknowledge the African sources for his books Why the Sun Was Late and Such Is the Way of the World, but I really enjoyed this story-poem, which is a story of Elkin's own making. It's not exactly a chain tale, but more of a long series, with the people of the kingdom doing everything they can to make sure there is absolute silence so the young king can go to sleep. Also, it is not told cumulatively one by one (although I think that would have been pretty cool!), but after every few items, Elkin does give a resume of the sounds that have been silenced, e.g. "No babbling brooks, no birds in nooks, / no ticking clocks, no clicking locks, / no shoes (just socks), no building blocks." Then at the end there is a repetition of all the silenced sounds, as you can see in the screenshot below, which shows the king's councilors, deliberating again after all their efforts have failed. 

I won't tell you what finally does allow the young king to go to sleep, but it is very sweet.