I personally really like a BIG Batfamily, but I do think the core group should be kept under 10 at any given time. I didn't care for the NuBatfamily, or any of their books. I'm not a fan of Bruce and Dick, to this day I boycott Babsgirl books, not out of my love for Cass and Steph, but for
respect to Oracle, Jason I wasn't a fan of at the time, and have only become on in Rebirth, I had no interest in seeing Damian with Bruce and not Dick...and there was NuTim. I don't need to explain NuTim.
So yeah, as a life-long Batfamily fan, like in most areas, the Nu52 was a rough time.
When Steph's Batgirl book first came out, yeah, I was pissed because I was hoping for another Cass ongoing. Still, I was and still am a Steph fan, AND she was Cass's best friend. I'd be doing nobody a favor by rejecting the book outright, and low and behold, it was a really damn good book.
As far as Babs endorsing her was concerned, she didn't at first, though not for the reason you brought up, and I've always thought the explanation was obvious: She's Oracle. She knows everything going on in the world at any given time, so while the reader didn't know, and Steph didn't know, Babs probably knew that Cass was acting as the Batman of Hong Kong (Which, while an incredibly seemingly racist move since Cass has very little if any connection to her heritage, DID mean that she was in charge of defending a much larger and more prominent territory than Gotham
Babs is Batgirl now, much as I hate that that's a fact, and even if there's a massive editorial and executive shake-up, the chances of ANYONE else becoming Batgirl again is slim.
But that's okay.
I miss Oracle, and I wish Cass could have her old Batgirl suit, and the fact that on paper we'll likely never see the Babs Cass mother-daughter relationship again stings (If they try giving Kate that role, my fury will not be containable)...but at this point, if they give me a well-written and drawn Cass solo book, and I will be able to ignore EVERYTHING else that's wrong.