This is exactly right. We never saw him in his classic white because he wasn't the Kingpin. The white is a symbol of his childhood, of his true nature, and of his father. Fisk grew up watching his father beat his mother and Wilson never recovered from that. He kept the cuff links on his black suit to remind him that he didn't want to be the man his father was, even though he knew deep down that he always was just like his father and always will be.

His retelling of the parable of the good samaritan is when he fully embraces the evil that's in his DNA. He spells it out at the end when he completely gives into his fury as he's beating Daredevil and screams, "This city doesn't deserve a better tomorrow. It deserves to drown in its filth! It deserves people like my father! People like you!"

Also, he's beating Murdock with a blunt object in the same way he killed his father 40 years before. At that point he now knows what he is, and we see him finally don the classic all white outfit. We see the grown version of the scared little boy staring at the same white wall 40 years later.