If we're honest, it's been hard to really see Doctor Who as the account of a role-playing game since The Dalek Invasion of Earth, or thereabouts. That's because it's about that time that the Doctor really becomes the hero of the show, and the other regular characters 'just' his companions. In the first season, he may have been the title character, and, to some extent, the focal point, but he was still more or less evenly balanced with Ian and Barbara, if not Susan.
But, from the second season onwards, he's much more obviously the hero, and that becomes even more the case once Troughton takes over and the mythology of the Doctor really starts to build. This works well in a TV show, but having most of the PCs be in the shadow of one of the others isn't such a good recipe for an RPG. The stories arguably also diverge from a 'gaming' look as they become more tightly plotted, again, from about the second season onwards.
Nonetheless, I'm going to stick with the analogy, at least for now. Because, why not?