i'm guessing she runs not so much because she's incompetent - but because she's an assassin, not a spy. at first it seemed possible that maybe her opponents are just more powerful than those she's used to facing because they're deeply involved with royalty - but in the situations she finds herself in, there's little to do but escape. she isn't supposed to kill any of these people so that's certainly not an option - not yet, at least. if she kills a small fry, it's hard to pick up on the trail since it's cut short; finding the mastermind is a priority. and there's no telling that her opponents will hesitate to kill her if she pursues a fight.
honestly, if anything, she's reckless. she doesn't watch from the side to obtain information, but provokes them to reveal more and more from close proximity. not to mention, she has to keep up appearances at the same time by constantly putting forth an image while being under scrutiny of the inner palace - which has little to do with just assassinating people and getting that over with.