Why He Should: Um... hes friends with Moffat? Also, he wrote the best episode of Sherlock, The Reichenbach Fall, which is something. Why He Shouldnt: Of all the names on this list, Thompson is most likely the one to garner the most fan backlash. His writing for Sherlock has been somewhat stellar, but hes also responsible for two of the worst episodes of Moffats run - Series 6's dreadfully dull The Curse of the Black Spotand Series 7's overly pointless Journey to the Centre of the TARDIS. Series 8's Thompson and Moffat-penned Time Heist was somewhat of an improvement, though, but theres nothing, as of yet, in Thompsons Doctor Who repertoire to indicate that he would be a good showrunner. The only thing keeping him in consideration? His close relationship with Moffat. Speaking of which...