She's one of the more down to earth members of the Superfamily, in spite of not having much of a civilian life. If Superman or Supergirl saves you, you'd be put at ease, but you'd still be too awestruck to form a coherent thought. With Karen, you're still awestruck, but she'd joke around with you to break the ice. Make you feel like you could go for a beer afterwards. She'd turn you down, of course, but the point is she's very personable and approachable.
And despite her unique situation, rather than just try to live normally like many versions of Supergirl, she started her own tech company in order to use super-science to help normal folk. Showing that kind of altruism in both her guises when she literally doesn't owe Earth-0 anything just shows how big her heart truly is.