Back to the theory that all girls are Sensei's daughters. I don't believe in this but I think the lineage issue is really important to the plot. So, what if all the characters do share a common ancestry, but at a rather weak level? Let's say all the characters had one original ancestor (god?) and it is because of their partial divinity that they can be named characters in Kumon-mi, have the potential to survive resets, and also attract the attention, one way or another, of the current gods.
But they are all on different levels because after a lot of years and generational changes, most families' bloodlines have become too diluted, which is why they have become "blind" and weak in relation to most things in Kumon-mi. In contrast to this, the Arakawa and Sakakibara families have saved much more and because of this they can see, hear and feel the true essence of things (I also think that they are much more influential and less defenseless to mysticism than they show us - I believe that they just don’t know how to show their abilities ).
Edit: This can also explain why the main and side characters are "immortal", while the same cleaners or Makoto's father are quite mortal.
I think this possibility is more plausible.
