I feel like Supergirl is a character that doesn't work in her own book unless she's introduced in the regular Superman story. I feel like DC made a mistake introducing Supergirl (and Superboy for that matter) the way they did in the New 52. It makes NO SENSE for Superman not to be involved with Kara more consistently given that they aren't only family, they are also some of the few remaining members of their entire species.
Kara is being written as a stereotypical rebellious HUMAN teenage girl, when she is actually a KRYPTONIAN who was RAISED on KRYPTON! This incarnation of Kryptonians are supposed to be so intelligent that they can have babies sit on ledges and not worry about it because the baies are too smart and well coordinated to fall off.
Kara up to now has been written in a really shallow way. They aren't thinking about how a teenage Kryptonian would respond to the tragedies that have befallen her. They aren'te writing her with nearly enough advanced highly evolved alien super-intelligence. I feel like there has been a complete lack of imagination and vision in relation to Supergirl. She should have emerged in an event in the Superman books that set the parameters for her stories in a way that made sense and united with the Superman books instead of having her go out on her own from the beginning. She's definitely a character that deserves her own book but she needed to be introduced properly. I just feel like she has suffered badly from the lack of united direction and vision early on in the Superman books.
There is so much wasted potential in her character its ridiculous. She should be written by people who have a grasp on high concepts and science fiction.
Supergirl is one character in dire need of a course correction in my opinion