He goes out to fight crime and ends up protecting people of all classes. From criminals.
Yes. It doesn't make him any less of a billionaire beating on people who have turned to crime because they were struggling to survive. That the reader is repeatedly told that Jason could've grown up to be a criminal is interesting in that regard; it's a reminder that Gotham is a social nightmare. That Gotham is poor and corrupt is as inevitable as the Joker staying alive, despite everything Bruce has been portrayed doing for social justice.
I'm not defending the criminals or condemning Bruce's actions, but privilege linked to money is inherent to the character. So in that sense, class issues are going to be a theme of his story.
Despite his other failings, I don't think Dixon can be blamed for how incompetent Steph was written later down the road. I think he was looking to create a contrast with Tim's character, and among the contrasts there was their social classes.