DbD:

So what if a series has a shallow premise? Azumanga demolished deeper series on the strength of Chiyo-chan’s and Osaka’s memorableness.

Jason may not see it, but Azumanga is a powerful tale of innocence. In addition, while in most series innocence is framed by contrast, usually over time, heroines of Azumanga do not have leave it behind and there's no story of loss of innocence, which lesser anime have to deploy whenever they engage the theme.

I want to remind everyone that this is not English literature class. You get no points on Derailed for analyzing anime like To Kill A Mockingbird.

Ah, but doing it sometimes helps against errors of judgement (of course everything can be taken to an absurd degree, but at least I do not call Azumanga shallow).