thinking back on what I said, this is actually one of the main problems with this show.
The girl power, and "I am my own character" mantra, is window dressing, when the show has totally ignored, and thrown away Supergirls entire history and identity, and replaced it entirely with "supermans cousin". That was the insult thrown at the character as a "ms male character". They inexplicably embraced that idea. Presumably to appeal to casuals that do only know her as that.
superman villains, superman friends. Livewire-supermanvillian, Redtornado-Justice league hero, Max lord-JLI hero/JL villian, MM-JL, Cat grant-Superman, Toyman-Superman villian, etc, etc. Non-superman2, Reactron-Superman, Jimmy olsen-superman, etc.
I'm not saying Supergirl's history isn't a mess. with multiple Comets, "her" being 3 different people(kara, matrix, and Linda Danvers)... her spending years in the 35th century(where most of her own identity elements take place...)
Powergirl is an inextricable part of Supergirl. Brainiac 5, as well.
The whole fish out of water, "I had Kryptonian powers for 15 years, but did nothing with them" opening is absurd, frankly. It would have been more faithful to rip off the Flash/Arrow a bit, and have the Legion of Superheroes or one of their villains show up and start it off. 16yr old Kara lands on Earth, gets adopted, and hides, while learning about humanity. 18yr old Kara is gets abducted and taken to the future. has Legion of Superhero adventures. returns to 21st century, right after dead superman, to help a world missing Superman, at 23 or whatever she is now. Can do, Arrow like flashbacks of her "on the island", can have cameos fro her future friends, etc..