I'm hoping that, once Bruce comes back to life and Babs vacates the Batcave, whoever's writing her at the time will do the perfectly standard comic writer thing and go "Babs's hangout in Gotham is the Clocktower, right?" and just move her right in out of sheer force of historical inertia, not even bothering to check if there's any reason that shouldn't work.

Because dammit, sometimes that impulse needs to end up as a force for good.