The young, somewhat irresponsible female teacher shows up in a lot of anime. Perhaps those traits make her less threatening of an authority figure to the audience?
Oh absolutely. Most authority-figure teachers are either not shown at all, have their faces off-screen (Charlie Brown adult style), or aren't really characters so much as... well, teachers (there's only one other recurring teacher in K-on, the old lady science teacher who only wears shiny glasses!)
where's my SoL about freshly-graduated teachers going into their first assignment at a middle-of-the-road high school? (class char designs would be hell... unless you pull a non non biyori and have a tiny school)