If you cut Leia's scenes, then you will end up with how her character ended up in ROTJ. To me, she is supposed to be a leader...after all, she is a Princess being groomed to rule a planet. Cut out her abilities to lead an army or participate and you end up with a damsel in distress, which is how I view her character in ROTJ. Would Han Solo or Luke have been that interested if she was a tag along?
Sorry if I'm late the party...been busy in recent times.