But what made him work, once Chuck Jones found the key to his characterization, was that it wasn't arbitrary -- he went to town on those who deserved it, who attacked him first or proved themselves to be bullies.
As punch lines to gags that were elaborately set up. They were paced out and given impact. That's not so much the case in this short.
Many of Chuck Jones's characters were defined by their obsessive refusal to give up in the face of their own ineptitude. They constantly sabotaged themselves, or they aspired to roles they were monumentally unsuited for, yet they persisted relentlessly anyway, so we could laugh at their folly yet still admire their perseverance. Jones's Bugs was the exception, a rare comic hero whose appeal came from his successes rather than his failures, because they were successes against people who deserved it and were executed with wit and style. He was the one character whose personal ambitions were below his capabilities -- just to lead a peaceful, modest life and trouble no one -- but who rose to the occasion in the face of others' aggressive ambitions, like Elmer's attempts at hunting, Marvin's attempts to blow up the Earth, etc. That's what made him a good foil for Daffy, who was so completely his opposite.