My comment to this post got long, so in addition to posting it there, I'm using it here, so I can have an easy post. It's a bit rambling, but I'm not revising it. Too lazy and too tired.
I grew up with Supergirl, pretty much in real time. So I have very definite feelings about the original Kara Supergirl. When she was killed in Crisis, I boycotted DC (except for Titans, which I read for 6 more years before I gave up on it due to its deterioration) and (except for the Titans as mentioned), didn't read comics for 10 years. That's how upset I was. Heck, I had LoCs published in the Supergirl comic! When she died, a part of me died, too.
I didn't read that Matrix Supergirl and only read Peter David's series toward the end because Kara, in some weird turn of fate, ended up on Earth and had to die back in Crisis to set time back on its course.
Yes, as I recally, the original Supergirl acted super before she told her foster parents she was Supergirl. At first, she was a complete secret, being super on the sly, but I believe she was out in the open for a while before telling the Danvers.
Was she wholesome? Hell, yeah. So was pretty much every character back in the '60s to some extent. And she spent plenty of time mooning over Dick Malverne, having a thing for Comet in his human form, and moved through the '70s as a typical female character of her era. Of course, it didn't stand out as much as some of the nonsense in Wonder Woman because WW was supposed to be one of the big 3 and Kara was just a "lesser" version of Kal.
They finally let her graduate high school, moved her through college, then had no clue what to do with her and that was the beginning of the end. In her own comic, finally, she worked for a TV station, to parallel Clark Kent's journalist job, then was returned to the college environment as an advisor where her stories were throwbacks to the '60s in many ways, the plots fairly frivolous. We won't discuss how many times she changed her super costume. Sometimes, it was issue to issue, and some were fairly ugly. And yes, while she was a successful backup character to that point, she was not successful as the star of her own title. I was relieved in a way when they cancelled it, because they clearly had no idea what to do with her.
I loved Kara dearly, but it took Crisis to make her interesting again. That's typical, as I've seen it happen on TV, too. Make a character interesting when you know they're about to die so folks will care more. And damn it, I cared, so much so that I never even read the rest of Crisis.
No, the new Kara isn't what she could've been and unless we off her and get a new one, or they come up with some sort of multiple Karas and the "real" one is the one who's left by story's end, this is the Kara we're stuck with.
When I got back to comics, I decided I had to let go of a lot of things that once mattered to me, feelings and memories, because retconning and rebooting had changed most of them.
This is Kara. This is Supergirl. I'm willing to let the current team develop her into an interesting, exciting character who will appeal to all ages. I like her trying to find her way. She has a horrible background to overcome, not the loving one the original had.
So she's not wholesome. I don't think it's written in stone that she should be. Other than Superman, who should remain noble, and Batman who should remain the avenger (though he's been redone more times than I can count), there is no character who is IMO immune to change. Even Wonder Woman has undergone personality changes.
I'd love to say that it's because the writers are men and can't write good female characters, or couldn't back then, but it was never limited to the female heroes. Batman has had his eras, too, from good natured detective (the camp years) to brooding and fairly psychotic avenger. Even Superman was tampered with, going through a soul-searching phase and probably others I missed during my boycott.
So, I'm hopeful Kelly and his successors, because there surely will be some, will be able to build something most readers can enjoy and make Kara real and interesting. I'm giving him plenty of time to do it.