I mean, what you are arguing is kind of the point of the character. Stain has a strong moral code and his conviction does have a point, Hero Society is based on fame and prestige and it seems most heroes do it for that, not for altruism.
Then again, he fucking murders people and is a danger to society. So the entire point of his character is that he has virtue but goes wrong about how he applies it. And he is saying stuff society is already thinking, when having a powerful, good quirk makes you better than others, while having a detrimental quirk makes you feared, even if you are not bad. While a weak quirk makes you "normal", almost a second-class citizen.
He is seen as "cool" in the video because the context of the video is him standing up to his convictions and stopping heroes on their tracks. Also why the series goes out of their way to tell you he is wrong.