I think ya'll are missing the stuff between the lines, here.
This is not about Kathy filling Joan's shoes, or the perception of Kathy "needing" to, or actually filling, Joan's shoes, either on the part of Kathy Griffin or the viewers.
This happened on the heels of the Giuliana Rancic SNAFU of making that stupid comment about Zendaya's hair and supposed "smell," at the Oscars, a "joke" which she reportedly made the camera crew record several times to get "just right" on camera, in order to keep the joke in the episode, and fully air. (Kelly Osborne quit after this protracted incident because even she has limits and knew it wasn't funny.)
The point is, I believe Kathy's quick departure has less to do with her style of humor--which is branded and known among any of her followers, including her haters, so, no surprise. She knows who she is and what she does, and wouldn't just up and quit if she felt she "sucked" or needed to refine her delivery. It has more to do with the fact that Giuliana Rancic is showing herself to be a vapid, insensitive jerk. She's also the managing editor of E! and has made them a boatload of money since she arrived, including the formation of "Fashion Police" from the get-go. So E! wasn't about to let that franchise go so easily. They probably still won't, unless Giuliana puts her foot in her mouth one more time and officially overstays her welcome. Kathy likely didn't want to work with her, the more she got to know her and her formula.
You've got your rich husband, rich career, and surrogate kid, Giuliana...just take your money and run before you keep sounding like a bigger jerk.
But Kathy Griffin couldn't just trash-talk a colleague like that. So, she made the classiest exit she could. I say, brava.
"There is no use trying," said Alice; "one can't believe impossible things." "I dare say you haven't had the practice," said the Queen. "When I was your age, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast." --Alice in Wonderland