Too many connotations. It bothers me tremendously that the Oracle had her own base, pretty awesome and distinctive in its simplicity, standing tall in stark contrast to the cave. I also believe the Oracle should just as easily be able to set up with her own resources and abilities as it would be to relocate out of town. Then there's the times that Steph used to hang out at the cave at Bruce's invitation, until Bruce decided to kick her out on a pretext. I feel like they would be welcome for as long as they want to be there, but that they don't really belong.