@hikarihenney I actually never thought of connecting those two (good catch!), and yes, maybe the author really did have more backstory prepared for Izumi that we didn't get to see. With Shirogane leaving for the Underworld and Saku and Tamamo in-charge of baiting the onmyouji, I just thought he left them in Izumi's care since he thought Kochou would be more comfortable with a fellow human.
Izumi's real name is Asano Tadashi and Kiizumi is his penname. Maybe he intentionally chose that penname after wandering into the Ayakashi realm so many times to anchor him to that realm.