Clara has conflicting inner needs. On the one hand, she absolutely needs to have control, to exercise boundaries and authority, which stems from her childhood experience of being “lost” and the eventual loss of her mother, who’d mitigated that awful experience. This, in fact, is the root of her sense of responsibility.
On the other hand she needs to travel, to explore, which often takes actually getting “lost” and letting go to really fully appreciate. She gets that opportunity with the Doctor, of course, but for the most part she’s been able to maintain more control over her adventures than just about any Companion before her — in part because she’s willing to let the Doctor take the lead when it’s obvious he knows better than she does; Clara doesn’t wander off, takes the responsibilities he gives her seriously.
She’s been able to balance (and indeed synthesize) these needs because she’s very intelligent — not just in terms of cleverness, but from having a philosophical attentiveness, the ability to see “deeper” than most. She understands how to navigate different social milieus. She understands how to invert her cognitive framework, from seeing that TARDIS is “smaller on the outside” to making Daleks “forget” to pulling a chair outside when the man she wants to talk to won’t come on in.
I would never think of Amy Pond ruminating on how everyone is a “ghost” from the Doctor’s perspective, on the eidos of a soufflé, or the soulfulness of an old woman’s remembrance of falling in love. Clara’s the one who recognizes that just because the Doctor’s learned to forgive himself doesn’t mean that the act committed was ever right, or fated.
So the charge that Clara has no “character traits” just comes out of nowhere. It’s an empty claim.
explains Clara’s character better than I ever could.