Captain America being known as Steve Rogers works because the other characters around him like Iron Man or Hawkeye aren't trying to hide their identities either. The Avengers are all largely pretty public about who they are, Tony Stark doesn't care people know he's Iron Man these days.
Dick Grayson being an unmasked hero makes things problematic for Batman (the more valuable commodity), because suspension of disbelief becomes harder around the issue of Bruce keeping his secret identity secret the more you look at the fact the public know Dick is Nightwing. It's why DC sort of quickly moved on after Dick was unmasked in Forever Evil, don't look to closely at the details of this, it doesn't make sense if you pay attention.