Sure, but All Might was saying the exact opposite and praising Izuku for being selfless just an episode ago. So it's just one of the messages in the show. In fact, if that was the main message of the show, Izuku wouldn't even be the hero because he was a quirkless guy who just got power because of his shounen heart.

A subversion would be something like Izuku failing the exam, becoming a vigilante, suffering from his lack of power, sacrificing his shounen heart to gain power, and then actually getting love and recognition after that. Y'know, like a less emo and miserable Archer.

Or just failing the exam. That alone would've been Madoka level subversion because of the show's title LOL.

Maybe he can apply as a janitor and become the strongest janitor alive after learning from many heroes in school outside of class.