So the only two options are campy and unrealistically uber grim and gritty? That's a pretty big false dichotomy as there are miles between those two opposites and all of them are not only creatively viable but have worked fine in the past.
But more to the point, no, I don't think the Joker or any other of Batman's (or any other super hero's) should be mass murders. The concept just doesn't fit with the idea of a perpetually ongoing series as it would force the hero to either kill his villains thus ending a fun tradition of reoccurring villains or else been seen as criminally ineffectual (which heroes like Batman have become when viewed realistically) neither of which are very interesting story wise.