I like Gatiss, but I don’t think he wants the stress. 
I think he also knows he might accidentally make it into the Hinchcliffe-era Redux Plus Plus, as that’s where his tastes lie, and he knows that can only work for so long and these days would skew to a different audience than the one the beeb actually want. 
I think that’s why he liked working with Moff, as it balances out where he knows he would go.
Like Moff, he does have a proper love and knowledge of the shows history, in that truly geeky way.
Something I actually think RTD lacks tbh.
		
		
	 
I'm not sure Moffat had anywhere near that knowledge.  He certainly didn't on 
Sherlock, where Gatiss could speak extemporaneously and knowledgeably about Doyle and the Canon in interviews, while Moffat could not and his level of knowledge about Holmes, Doyle, and the Canon seemed to be more folk memory.  (There was one interview where Moffat talked about Moriarty in the Canon, and I wrote on Facebook, "Has he even 
read the Canon?")
I'm not saying Moffat wasn't knowledgeable about 
Doctor Who, but it always seemed to me like a very idiosyncratic, rooted in 90s fandom and USEnet culture knowledge of 
Who.
That said, I'm not sure a showrunner 
needs to come to the table with a deep, intimate knowledge of a property.  Today, there are references to 
everything, and everything (or close to it) can be rewatched and dissected endlessly.  Harve Bennett and Nick Meyer had very little knowledge of 
Star Trek in 1981, but they educated themselves and made a damn fine movie.
Do I believe RTD was a childhood fan?  Absolutely.  Do I care what level of personal knowledge he brought to the table twenty-plus years ago or that his NA collection might've been for show?  Not really.  The results spoke for themselves then.
The necessary skills are the ability to write, write well, and produce the show.  I know this will be controversial, but being a 
Doctor Who fan is 
not a necessary skill for being the 
Doctor Who showrunner.  If RTD's successor is someone who's worked in sitcoms for a decade and 
never written 
Doctor Who or even expressed an opinion about it, I'm fine with that.  
Doctor Who can be learned.  The writing and production skills are the ones that matter most.