Why is he not allowed to ever show his face? Can't he take off his helmet when he's at home? Does he wear the helmet to sleep and in the shower?
Judge Dredd is a parody/homage of the laconic American action hero, the loner-riding-into-the-sunset type. He never shows his face for the same reason Clint Eastwood never tells ya his name in a Spaghetti Western. He may dress as a cop but maybe he got The Man With No Name confused with Dirty Harry. It's the same guy.
If that doesn't work in movies, then the premise of Judge Dredd
doesn't work in movies and we'll have an interesting failure.
However, I also expect that the movie won't lean too heavily on Dredd as the lead character and there will be other characters in the story whose liveliness and abundant personalities (I can think of many examples from the comics) will more than compensate for Dredd's lack of visible persona.