Why does Shichika allow Princess Hitei to travel with him?
Princess Hitei released Togame from her burdens and sent Shichika to thank Hitei for that. Hitei also confessed that she didn't dislike Togame. Hitei also was going along with the motives of her ancestor, not her own volition. So in a way, she killed Togame for two reasons, to alter the future and to release her from burdens/responsibilities. She semi-respects Togame in the end by cutting her long hair as short as Togame's. Even Shichika has a shred of humanity to realize that any needless killing is well, needless.