Further: why would the checkbox exist in the first place, if it doesn’t work anyway? If this is truly something that cant be done, the checkbox should be removed or a little informational box should be added to the paging extensions main information page stating that it is unable to be published, etc.

I initiated this feature request and I think the wording and details should be changed a bit. While the "publish in company directory" checkbox works for users and queues, the issue is that for Paging Only extensions, even though the "publish in company directory" checkbox is checked, it doesnt actually publish it in the directory for people to add as favorites in their HUD on the App. The explanation by tech support is this: User extensions and call queues are designed as fully functional communication endpoints capable of routing, initiating, and receiving standard inbound/outbound traffic. Because they interact natively with the softphone interface, checking that box provisions them across all endpoints, including the RingCentral app.
In contrast, Paging Only extensions are fundamentally different. Because the RingCentral desktop and mobile apps do not natively support receiving audio pages, the product logic purposefully prevents these extensions from syncing to the RingCentral app's interactive contact directory to prevent users from trying to message or directly dial an unrouteable endpoint.