Let’s imagine you’re an inventor on a planet far from Earth, a planet called Xeriphas (which is almost Sapphire X backwards, a fact that wiseacre visitors never tire of telling you). And you’ve come up with a rather brilliant robot. He (for it is definitely a he) can change his shape at will, becoming a replica of anyone you wish. You’re quite a bossy inventor, so you need your robot, which has his own artificial personality, to follow your whims right away.
Maybe he’ll have had more free will at first, but proved to be a little too wayward to be of any real use. You’d be all: “BECOME ELVIS PRESLEY” (or Xeriphasian equivalent), or “BECOME THE XERIPHASIAN HOTTY I NEARLY KISSED AT MY FIRST HIGH SCHOOL PROM, THE ONE WHO LEFT WITH THE RESERVE QUARTERBACK AND IS NOW REGIONAL MANAGER AT XERIPHASIAN FOOTLOCKER”, and he’d present you with Chewbacca, for a laugh. That’s no use to anyone.
So, you’ve made this robot, he’s at one and the same time a companion, and all of the companions you’d ever need, rolled into one. And you decide, for reasons best known only to yourself, to name him Kamelion, after a remarkable animal which only exists on a planet many light years away: the camel-lion.
I’m joking of course. He has a chameleonic ability to change and blend into his surroundings, exactly like the TARDIS doesn’t, so of course you’re going to call him Kamelion, in the same way that a Time Lord might decide to call his robotic dog K9. And as you’re such a literal person, you’ve probably renamed yourself Professor Ian Ventive, or Ivana Thinkalot, just to keep casual visitors aware of what is what.
Anyway, your problem is this: what happens after your robot is stolen by the Master and taken to 13th Century England to become a fake King of England? I mean, how can you be sure he’s really gone? Do you find yourself wandering up to strangers and trying to will them back to robot form? Would you construct some kind of Kamelion-spotting device? It’s a puzzler.
Meanwhile, the rotten old Master has set up your robot, YOUR robot, as King John, and only the intervention of the Fifth Doctor has saved the day.
But does he return Kamelion to you? He does not. Free from your needs and the Master’s bizarre commands, Kamelion does what he’s programmed to do, and submits to the will of the nearest dominant adult, namely the fella in the cricket gear (for now at least):
The problem is, being a very passive sort, there’s not really a lot for a shape-shifting robot to do aboard a time-machine, and when he’s in robot form, he becomes kind of clunky and fragile-looking, not the kind of figure you need in your team, while striding around a rocky outcrop. And, oddly, this Doctor fella seems to forget to make him turn into a mountain-climbing action man when he leaves the TARDIS, so often he’s left in there alone, like a dog in a hot car.
In the end, that Master fella comes back and takes him over again, and he gets so fed up of being bossed around all the time he begs to be destroyed.
So, in a series where the Doctor famously picks up a companion and changes their world-view entirely, usually for the better, Kamelion remains the only one for whom change is a fundamental part of who they are, and who simply cannot handle it.
Maybe you should consider making a less sensitive model next time?
PS: For the true story of how Kamelion came to be commissioned, ignored and then destroyed, watch this (slightly muffly) DVD extra from The King’s Demons: