I think I'm starting to see the reason why Hana is in the manga - without Hana, Mieruko would be spending forever ignoring all the spirits - and who knows, maybe her mental fortitude might be strong enough to hold out.
But thanks to Hana being present and getting sick from this teacher, I think that Mieruko will probably at least connect some dots and realise (at bare minimum) that ignoring the spirits in this case is not viable.
It's more surprising that this is probably the second time that Hana has been around certain spirits for prolonged periods of time. With her being a living spirit feeder, you would think that there would be other spirits like the first one that would stick around her just to eat off her life energy. And even speaking of that first one, that one didn't make Hana so burnt out like she is now...