What do Haikus in Ghost of Tsushima do and how do they work?

There are places in the world where you can compose Haikus. I've done that three times now, and the only result seems to be a headband received for each. Those seem to be purely cosmetic items.

Does it matter how you compose the Haiku? Are all results the same, or is there a "correct" choice?

Solution 1:

There is a trophy for doing all the Haiku sites (you also need to visit various other sites):

"Body, Mind, and Spirit" visit all Hot Springs, Haiku, Inari Shrines, and Bamboo Strikes

Other than that I think these are just intended to be a moment of reflection amid all the fighting.

There doesn't seem to be a correct choice, and the headbands (and other hats) are just cosmetic.

Solution 2:

Just the theme counts here.
It will determine the look.
Your choice sets the text.

(I'm horrible at Haikus, so, yes, they won’t change visually, but the game remembers your choice for the flavor text. There’s no wrong or right.)