^ The amount of villains that the Kara Zor-El Supergirl has that are exclusively her own can be counted on one hand.
She really is intrinsically tied to Superman, so what they ended up doing was to take characters from the "Super"-mythos that are more traditionally associated first and foremost with her cousin and repurpose them in a way that associated them specifically with her... and I don't see that as a bad thing or as her 'living in her cousin's shadow'.
What it means is that the comic SG was never developed well enough to have many memorable storylines or villains, hence using Superman's. So, one cannot honestly say that SG was established as her own character.
Now, when it comes to a
general influence--approach--that's another matter. When interviewed about
Supergirl, Berlanti said how much he was personally influenced by the approach to a superhero in the Donner
Superman, and I found that was promising. In other words, he was talking about essence of how superheroes should be brought to film--that, and a few visual nods from
Superman the Movie. I posted comparisons in the season one thread of that, but I wanted the series to use that general influence, while establish its own identity where villains and story were concerned. She should have been more of the larger than life anomaly taking her status seriously in a
very ordinary world. Only a few episodes touched on that--usually with James driving that dialogue (that was fine for the James / Kara development) but that's not taking entire characters or stories from Superman, just an essence.
I wish the series would build on the greater, serious feeling an alien hero would generate in the world. Hell, even deep into the MCU with
Civil War, those discussions and feelings are still an issue in that universe.