I think they are going for enthusiastic, which after EONS of disinterested or even remorseful, apathetic, or downright unwilling heroes is also refreshing. But still, when she is smiling while being tied up by gun toting thugs it defuses the menace a bit. I did like that the mom called her out for being "rich and young" and how that makes her very unaware of life in general, so there is that character flaw as well (assuming that IS a flaw on the show). Maybe a few rounds of torture will give her some appreciation of life's fragility.
I don't THINK they are portraying Kate as foolishly reckless and irresponsible, but if they are going for stubborn, headstrong, and (over)confident then they need to have her lose some and grow a bit.