I'm kind of amazed we haven't seen Booster Gold on Legends, he seems like the perfect character for it.
The movie division has been developing a Booster Gold script by Zack Stentz for Greg Berlanti to produce and possibly direct. It's in limbo after Justice League's lackluster performance, but maybe it'll go forward if Aquaman and/or Shazam! do well. So the character is evidently off-limits for TV. (It's the same reason Brandon Routh plays the Atom instead of Blue Beetle. He was going to be Ted Kord at first, but there was a BB movie in development, so....)