Your are correct. Its also the same for pigeons. I keep a few pet pigeons and all the advise was they need flat platform type perches to roost on.
They were always getting covered in poop and the birds would walk in it and then fly about walking it into everything else they landed on.
I replaced them with thick branches - similar to the one your chickens are on - and everything is much cleaner and the birds can roost on them easily and comfortably.
Nevertheless, the flat perch may be cheaper to acquire or make and install. Besides, 2-1/2 inches in diameter is rather large, almost the size of a bean can.