That was actually another part of the game I thought was really dumb. What does Batman, or anyone else, care that his identity is out? That he was scared on TV? I guess the next time he run into a villain they're going to say "Nah, I know you're Bruce Wayne, you don't scare me any more!" right before they get punched in the face? He still has the intellect and resources.
With Spiderman keeping his identity hidden is supposed to keep villains from attacking his friends and family, but as seen in this game everyone Batman cares about also openly fights crime, so what's the big deal?
I agree with you that Rocksteady has to have meant the torture scenes as the Knight reveal unless they think very little of their audience, but then why beat around the bush for another couple hours? And like you already mentioned, as someone who has very little Batman experience outside the games that character meant absolutely nothing to me.
A stoic person who doesn't kill on a revenge mission is basically the definition of Batman