Why does Azumanga Daioh have the category Iyashikei? This is no more a "healing" story than Lucky Star is, and that page isn't tagged with the category.
Topic on Talk:Azumanga Daioh
Right. Removed the category. Maybe it could be Iyashikei if Yukari-sensei, Tomo, and Osaka were all removed (the last on account of "I was the murderer!").
I tend to think in terms of crossover fanfic. Iyashikei stories are those which, when crossed over with any other story, become the genre of that other story. Not because the characters are weak or anything, but because the plots are so mundane that nearly anything is more important than what these characters normally do.
Yet Tomo and Yomi alone can turn most any situation into Manzai.