See, I don't know about that. On one hand, the mask was his attempt at emulating Batman and since his idol basically told him to **** off, you could make a case for him shedding it. By that same token though, like you said, it is indeed now the face of The Riddler, for all intents and purposes and sets him apart from previous versions in a very big way. So when you spin it like that, I can see it staying.
I also feel like Penguin's a different case. He lives a lavish lifestyle and has his eye on the mayor's spot, yet has a skewed reference point of the kinds of circles such people could afford to run in, hence his childhood love for Fred Astaire and dressing in a tuxedo to "play the part" of a member of high society.
Nashton doesn't really have that. He's a downtrodden member of the lower-class who became a murderous terrorist after witnessing Batman in action and dressed accordingly, in his own way. The only way you could really rationalize him wearing the classic outfit is The Joker influencing him, either intentionally or subconsciously. There's a level of rationalization beyond just "They look like that in the comics" (not implicating that you're one of those people btw, just a minor vent generally-speaking).
