A 1970s setting may be where , it allows Kara to be introduced on her own and without worrying about the larger (and sometimes confusing) continuity of the DCEU. It would also continue a trend Wonder Woman began to give female heroes origin stories that are prequels to the larger universe. Marvel is doing the same thing with Captain Marvel taking place in the 90s, and even Black Widow is reportedly an origin story. But, since Supergirl is still very early on in development, the 70s setting may very well change.
Source: The Playlist