I do see that K-9 now has enough nostalgia value that thirty-somethings who remember him from the past can sit down with their own toddlers and enjoy him on screen. And there must be something going for the character for him to have stuck around for so long.

But I do think he shows the signs of being what he was - a gimmick designed for a single story, seized upon by a production team desperate for a new direction, being under instructions that they absolutely could not continue the 'gothic horror' mode of the previous three years. It evidently seemed a good idea at the time, but caused endless problems for writing Doctor Who. Not only did one have to shoot in such a way as to get K-9 and the actors in the same shot (hence lots of crouching), but the prop could move no faster than walking pace, so couldn't be included in 'chasing down corridors' scenes. It was even more useless when it came to location filming. Hence the years 1977-81 are littered with stories that begin with some contrivance to take K-9 out of the action. If it is only the upcoming K-9 series that made the producers of The Sarah Jane Adventures decide to largely leave him out, I do think it's a blessing in disguise.