Well, I'm not sure if Edge was going to kill Kain but he was quite mad at him and still thought of Kain as a traitor after the Giant of Bab-il was destroyed and they discussed if they should forgive Kain in the Lunar Whale. Even though Rosa probably didn't stop Edge from killing Kain she at least convinced Edge to let Kain fight alongside them and make Edge realize that the evils he commited weren't his fault since he was controlled by Golbez who was controlled by Zemus.

Also, I totally understand your frustration since that happens here on EoFF quite a bit. Even if it's just a game biasedness is always quite irritating no matter what it's about.