I have yet to find a fic where Jaejoong is depicted as someone who isn't a bad boy. He and G-dragon get the same tropes. Both are mafia members or cold adults who were surprise, surpise, abused children. Or maybe they're the most perfect, cold dude... I am pretty sure that it's coz of their appearance. Their flaws are so expected that they don't look like flaws anymore. Both guys are considered 4D, there's so much in their character that can be utilized. If we're gonna use their names for fiction better make the most of it really. 

The way to enjoy a treat is to rip open the package.