Oh my god I have so many feelings about this.
First of all, while I think it’s fair to acknowledge that traveling with the Doctor does give Rose a sense of purpose and direction and helps her reach her full potential, I really don’t like saying that she NEVER would’ve grown to her full potential if she hadn’t met the Doctor. Plenty of people start off in jobs they find unfulfilling and, through their own initiative, find something else to do with their lives that they find more fulfilling. We don’t need to meet a 900 year old alien with a time machine to do that.
But I also find a lot of problems with the assertion that the female companions reaching their full potential through the Doctor is patriarchal in nature.
First, the companions don’t necessarily change becauseof the Doctor; they change because of their experiences traveling through time and space. They discover a lot about themselves by being put in incredible situations that wouldn’t happen to them on Earth. They discover just how strong, courageous, and passionate they can be. And they discover a lot of this in the Doctor’s access.
Now, a valid criticism that can be made of this argument is that they can only access these experiences through the Doctor, who is the only person who can pilot the TARDIS and provide them with these experiences. But I would also point out that the Doctor helps all of his companions reach their full potential, regardless of gender. If only the female companions were transformed by their experiences and the male companions started off amazing and remained essentially unchanged I’d agree that this was patriarchal, because the men would reach their full potential on their own and the women would only be able to do so through a man. But the Doctor helps all of his companions reach their full potential by putting them in situations where they can discover their abilities on their own, and occasionally giving them additional encouragement and support.
The ultimate lesson of Doctor Who is that everyone is important and that anyone is capable of being extraordinary in the right circumstances.