I personally think that this is a terrible idea. Supergirl at her best is not a stand alone character. She only works when Superman is around to serve as a mentor. After all, unlike Clark, Kara did not grow up on Earth and arrives as a teen/young adult. She usually requires the presence of Clark and or the Kents to ground prepare her for an earthly existence.
There are characters that are better suited to a solo existence. Supergirl was likely only chosen for the name recognition.
That's the way it's been done before, but I don't see it being a necessity for the character (just like it's not a necessity for most male superheroes who don't have a mentor to teach them how to use their powers, or have other superheroes to interact with).
And plus it could even be more interesting watching her have to figure things out and adjust to life on Earth all on her own-- something which I thought the New 52 comic depicted really well (yeah Superman was in the picture, but she wanted nothing to do with him early on).