Reiger hadn't forgotten the purpose of his visit to this world and the successive trips he made through Dimensional Travel.
It was to level up and acquire the strength needed to be called a Sword Saint in the continent of Akasha.
Unfortunately, this world did not have a formidable opponent that could help Reiger achieve greatness, including the two demons that had previously sparked a slight interest in him.
The Upper Moon One, Kokushibou, was very strong, but he was only a Lv.5.
Kibutsuji Muzan was very strong, but even after consuming thousands of people and gaining sufficient enhancement, he was still merely a Lv.6.
Such demons were indeed powerful to the rest of this world, but to Reiger, who could take down a Lv.6 even before coming to this world, they were somewhat less impressive, let alone after he had upgraded the Sun Breathing technique and gained the stable ability to surpass one level of combat power.