Akane doesn't care that Jouji proposed to her on day one, doesn't care that he's relentless, doesn't care that he'll wreck a mecha just to prove something, and that refusal to perform the role of the love interest is the entire show. The mecha gags work because they're built on the same joke: watching someone who actually has a personality stay unmoved while everyone around her loses their minds. By the time you realize how much Akane's coldness costs her, the show has already made you stop laughing at her and start watching her survive it.
Jouji Gouda transfers to Hakuryo High and falls for Akane Suzumiya, his class representative, the moment he sees her. On his very first day at the school, he proposes to her. Akane finds him extremely irritating, but the hot-blooded, simple-minded Jouji refuses to be discouraged and keeps hunting for new ways to show her how he feels. The three-episode OVA mixes comedy and romance with mecha elements.