The communicators were, unfortunately, a victim of the inconsistent Trek technology. There was never a consistency to whether or not intra-ship communication was handled by comm badge, comm panel, or just used the same interface that they use to talk to the computer. In one episode, a character will hit their comm badge to signal the bridge. In another, they'll go to a computer panel in the corridor. In another, they just announce who they want to talk to and the computer seems to understand and route it.
So who knows if a comm badge would be necessary or not on a starbase?
So who knows if a comm badge would be necessary or not on a starbase?