I learned most of what I know about storytelling from improv. Fortunately I studied improv with people who were less interested in making people laugh and more interested in telling a good story. One of the things that was hammered home to me over the years was that the most important ingredients for a good story are characters and relationships not plot. If you have the first two the third either doesn't really matter or will come naturally.
Lots of things go into making good characters and relationships, but the cornerstone really is a character's motivations. Looking back at all of the companions in the Doctor Who reboot, the most interesting ones had the most interesting and complex wants and needs.
On some level most companions are looking for adventure. This was certainly true of both Donna and Rose. They both wanted to get out of their dead-end lives and see the universe. Rose also wanted to protect her mother and reconnect with her dead father and... well she didn't even know what she wanted from Mickey, but that made that relationship interesting. Whereas Donna wanted to protect her grandfather and get away from her mother (while still craving her approval) and find a husband.
Martha, on the other hand, wanted the Doctor. She too had relationships with her family back at home, but mostly she was just in love. This made for a rather one dimensional season as all you could really do with that was shit on her while Ten ignored her and pined away for Rose.
Amy wanted her "raggedy doctor" to be real. That was perhaps the initial genius of Steven Moffat's takeover of the series. He takes over a series with millions of adult viewers who watched the show as a child and fantasized about what they would do if they traveled around with the Doctor. So Moffat gave those viewers a companion living out her childhood fantasy of traveling with the Doctor. A fantasy that was so all consuming that it was getting in the way of her living her life to the point that she ran away from her wedding to sort it out.
Rory on the other hand, just wants to be with Amy. He loves her so deeply that he's willing to travel to the ends of time and space to protect her and be with her (or spend thousands of years guarding her while she's trapped in the pandorica.)
That was an interesting dynamic for a couple of seasons but couldn't sustain itself very long largely because Amy and Rory had no relationships outside of each other and the Doctor. Eventually we had a few interesting episodes with Rory's father, but we never really knew Amy's parents, largely because they didn't even exist there for a while. Then we had Amy and Rory's kid and River Song add a little complexity, but towards the end things just sort of puttered out.
Now we have Clara. She's been around for half a season and I have absolutely no idea what she wants. She doesn't seem to have a particularly onerous life back on Earth in the present, that we know of anyway. Although now that we've spent an episode with the kids she nannies, I wouldn't blame her for wanting to get away. Except that even in that episode, Clara and the kids were rarely in the same scene together, so we never really got a sense of that relationship to each other. So really, the only relationship we've seen Clara have has been with the Doctor, and I don't even know what she wants from him.
That's why, as I watch this season with Clara, I keep feeling like there's nothing there or there's something missing. She has no motivation. Nothing is driving her. Nothing is moving her or her story forward. Without that, her character doesn't really exist, and without characters, the story's not going to be very good.