She can be viewed as symbolic of the ineffectiveness of educational institutions imparting any truly important or useful knowledge: Naota constantly characterizes the adults around him as "unable to grow-up". In his mind, Miya-Jun's inability to act like a normal adult (similar to his father, grandfather, Ninamori's father, Amarao, and many others) confirms his theory. Adults like her are contradictions in Naota's life; he wants to become an adult, but the adults around him don't act like adults at all.
A recurring gag is Miyaji's car being destroyed by a robot. In Episode 3, her red Volkswagen New Beetle is crushed when Canti jumps down on it from the school's roof. In Episode 6 she has replaced the old car with an identical one, but it gets eaten by the Terminal Core.