I think the bolded part is important. Some writers that are called to replace the old one (s) can say 'Oh, yeah, I respect the source material of the original writer, but I think I can bring something new to the people by exploring other paths that have not been walked before'.
I would usually question myself if they are still in touch with the old writer (or at least have an idea of where he wanted to plot and characters to move towards in the future).
Take for example, say, X-Men (I'm sorry for derailing the thread; I'll try to be quick). More specifically Grant Morrison's.
He wanted Magneto to become a full on psychopath (mostly because he seems to dislike the character), so he had him (an Holocaust survivor) pushing humans into ovens while high on a drug or some shit like that that I can't remember very well right now. When his run ended, other writers (that did not dislike Magneto as much), tried to retcon the whole thing, creating one of the biggest messes I've ever read in comics before I decided to pretty much quit on them.
If, say, I were brought to the team in order write some scenes and Cheeky said:
Cheeky: You know what, zajaz? Do whatever you like with X character. You have full creative liberty to do what you please.
Me: Really?
Cheeky: Yeah, sure. As long as said character ends up with the MC if the players choose to, I have no problem.
Me: Well, I've wanted to explore a kink with Monica...
Cheeky: Sure, go ahead. Whatever you write goes.
Me: Sure thing boss.
*I proceed to write about how Monica used to be a call girl in her youth, in full, glorious detail to satisfy the NTR crowd*
Cheeky:
Me: Oh, yeah, that's nice.
It's important to keep in touch or, at the very least, know where the writer wanted the characters to come from, so you don't write stuff that's overly egregious and / or contradicts previous hints or dialogue.
It is also important, I think, that the writers don't be too much biased when it comes to the characters; that can be hurtful to the overall project. A new writer that hates Wanda, for example, and is given full control over her without any kind of overseeing from the higher ups can lead to a distaster, IMO.
Nonetheless, I must say that I like the way that you guys are in synch with one another. I hope I can see much of your work in the near future. Cheers to you.