To your suprise, Upper Moon One - Kokushibo, was a pretty good travelling companion. But you still weren't sure why he choose to betray Muzan and travel with you, in the first place

Your situation was similar to that of Tanjiro's and Nezuko's. During the day, you carried Kokushibo around, in small wooden box, and during the night he would sometimes help you slay demons. The only exception was that Kokushibo wasn't wearing a bamboo muzzle on his mouth, like Nezuko