That was my point. It shouldn't matter to us either. I think most of us (including many writers and editors) bring too much baggage to the character and can't enjoy an obviously well-designed update like the current cartoon incarnation.
From what I understand (I haven't read any SG since Crisis), Peter David was trying to graft a new character of his own onto Supergirl. Other writers have been trying to get around the DC rule of "only one Kryptonian" in similar ways. In future, they should stick to versions of the current (read: original) model.
Because they ARE kids, Telle -- for the most part they haven't been exposed to the "Supergirl heritage", nor does that matter much. To them, the animated Kara In-Ze is THEIR Supergirl, which is why DC forced Linda to abandon the "classic look" and don that cropped t-shirt costume late in her series.
But you know what? I don't mind at all if these kids accept Kara In-Ze. In the animated cartoon and related comic book she is a perfectly legitimate Supergirl with an origin that actually works better than the "flying Argo City" of yore (which originally didn't even have a pressure dome to keep the air in!) And she has a sassy but appealling personality -- essentially sweet, but with a "hip" contemporary style that's not too "edgy". Right now I'd prefer her to the current Kara Zor-El, who hasn't really shown much of a personality.