Oh god....I didn't even think about it but maybe the MoM really WAS telling the truth that he's too scared to ever take his off. But not because he's afraid of the darkness but rather in order to eradicate darkness just like Xehanort he'll have to wipe out all the hearts with darkness in them. Maybe his plan won't even allow him to choose who gets wiped out just that if there is darkness POOF they're gone. If that's the case then the MoM's actual reason for the coat can be interpreted "I'm to scared of Oblivion to take off my coat, I have to keep myself pure so I won't be eradicated when I execute my plan".
With the chess game you make a good point but I think it's more than just Sora. We have the MoM and his Foretellers remnants of a time in which darkness was the ultimate evil that needed to be crushed at any cost. Then we have Darkness who comes from a time in which the light created it then fearing what it created tried to wipe it from existence and that's sowed a belief that the darkness will never be safe so long as light persists and thus it seeks to wipe out the light. But then you have Sora's group who has been forged in light and darkness.
Sora is a light who never goes out but isn't above tapping into the darkness and doesn't hate the darkness. Kairi is a strong light as pure as they come but she's never feared the dark, be it hugging heartless Sora or jumping headlong into a corridor of darkness Kairi is light but without a fear and hate of the dark despite having every reason to. Riku is a being who exists in perfect harmony of light and darkness, bringing out the best of both and showing everyone who meets him another way than extremes.
Roxas, Xion, and Namine are beings born belonging to neither dark nor light and are aligned with neither. They are born from darkness but live in the light, they belong to the dark but they are good people who live amongst those of the light with little issue. They are an in between existence and their two other members Axel and Saix while born as people of light, have lived most of their life as in between beings which makes them able to understand both. Neither fear light nor dark they cross an intermingle with both forces. Just as the Sun sets and brings the dark and the moon is the light that lights up the dark.
Terra, Aqua, and Ventus were raised in a very light stringent home but in the end they've all learned the folly of that. It left Terra with deep self loathing issues and anger he could not control. It left Aqua with serious repression issues unable to handle it when her heart started to crack. It left Ventus feeling burnt out on the whole light and dark thing in general and just wanting to be a person of his own choice. Each of them fought against their darkness but it never solved the issue, instead it was their fight against the dark rather than an acceptance and dealing with it that lead them all to their tragedies they needed to be saved from. Now though they leap headlong into the darkest most dangerous realm we know, the realm of darkness, with a smile and almost eagerness.
Our heroes show the full spectrum of bad, good, and the middle area between the two. The follies of light and darkness as well as their strength and potential of unity. They are products of the world where light and darkness co-exist, they don't know another existence other than this one. Which is ultimately why they are a rejection of extremes, they together can create a balanced world where light and dark exist in harmony.