That's how they make Oracle more prominent? Don't give her her own base of operations? That seems to me like a major need that Babs would certainly understand and find important. Why can't it be about the basic need of a character's base of ops instead of about: Oh! The Batcave is awesome! And look, Babs is using it!
How much do you want to bet that the big confrontation between Babs and Dick is Dick discovering she and Steph have moved into the Batcave?
Isn't it supposed to be empty now? And how come the greatest computer expert DC has is using Bruce's computer instead of her own? She could hack into his from an old frozen orange juice can and a piece of string, but using the cave feels like they're trying to add substance that belongs to somebody else instead of going for her own strength.
I also think it's disrespectful to Bruce. I don't think he'd like Babs and Steph making themselves at home and I hate that they're writing her as okay with it. I doubt DC has thought that far ahead, other than the possibility of cool!confrontation, but it's not a very strong choice for Babs.