in short i think that gryffindor is an easy but superficial reading of izuku as purely “brave” or selfless… there’s nothing wrong with wanting to accomplish something to empower yourself! we see over and over that izuku isn’t just motivated by pure selfless courage, and that’s totally understandable and respectable given his lifetime of subjugation.
even though he thinks little of his own safety he does so to achieve his ambitions – we see that he’s self-preserving in situations that have nothing to do with his ambitions, yet he puts his own safety on the line over and over for his ambitions even in situations where no one else is at risk. even when he basically throws the match to todoroki, it’s because he feels “frustrated” that todoroki wasn’t looking at him and treating him like an equal opponent. it’s the nicer iteration of bakugou’s same frustration with todoroki. it’s kindness, but it’s not just kindness. he consciously imitates bakugou’s moves and even his foul mouth multiple times even though he hates him and thinks he’s a bad person, because he sees him as strong and he wants to become someone who can take bakugou down.
he’s crushed when all might recommends other ways that he can help people, because even though he wants to help people, he doesn’t JUST want that. he specifically wants to be a hero. not just “a hero” but the greatest hero. if all he cared about was helping people, he would be happy to be a sidekick, or even a police officer as all might suggested. but he’s not. that’s not just bravery, that’s ambition. and he pursues that ambition with cunning. pure slytherin. i think ignoring all that and reducing izuku to pure kindness and courage, while ignoring his frustration and bitterness about his trauma and his determination to be freed from his situation, is doing him a disservice as a character with depth!