She was a co-founder of the Inquisition. Currently, she uses her combat skills to advance the cause(s) of the Inquisition while leaving all of the other tasks to people better suited for the job -- spymaster, diplomat, military commander.
Sounds reasonable to me. It's better to have someone who knows their limitations than allow themselves to be promoted to the level of their incompetency when there are other people better suited. Note that I'm not saying Cassandra would be bad at, say, military commander, but Cullen does have more experience with military structure and organization than Cassandra does.
I kinda feel that way about the Inquisitor sometimes, to be honest. Well, I suppose it depends on RP and background. I think the reason for promotion to Inquisitor is pretty thin. Half of the reason people are blindly following is because they're the so-called Herald of Andraste rather than any sort of demonstration of ability. One of the best examples of this is in the tutorial prologue when you are consulted about whether to take the mountain path or the more direct route. You can say, "Now you're asking what I think?" Their response is basically that you're a third party who can make the decision, since we're at odds, and we have to protect you anyway, so you might as well. Not the best reason, but there ya go. It just goes from there...
At least with DAO the only other Warden was Alistair, a similar "new" recruit, less than a year after his own Joining and also just 20-years-old. In that case, it never seemed much of a stretch that people would defer to the PC Warden since Alistair is reluctant to take on a leadership role.