Ironically then, Tom Baker was NOT a fan coming in to the show, and he stayed the longest. You can argue that the actors who were the biggest fans of the show were Tennant and Hartnell himself, and they only stayed "average" tenures, albeit for different reasons.
Personally, I would rather hope that Capaldi's status as a superfan would result in a BETTER tenure, over his having a LONGER one. A decade or more from now, I'd think any actor - and most fans - would rather remember an era of Doctor Who with words like "Capaldi's four years were the best in the history of the show", versus "Capaldi's eight years marked the longest continuous time an actor held the role".
Mark