They generally are!
Some systems required the sender to select a geographic region to increase bandwidth efficiency, or alternatively the pager owner to update their coarse-scale location with the operator after moving significant distances.
The latter is what the old Iridium satellite pagers did (do?), for example. (Not sure how the new GDB-based ones work.)
I think the service is finally being decommissioned due to the Iridium Next satellites not supporting it anymore. It has been supported for more than a decade without onboarding new customers though.
Apparently that's optional:
> Iridium Burst-enabled devices can be configured as receive-only so that no transmissions are made, a feature valued highly by some customer segments.
(from https://www.iridium.com/services/iridium-burst/)
> I think the service is finally being decommissioned due to the Iridium Next satellites not supporting it anymore.
If that's the case, it would have been inoperable since 2017 – they deorbited the old satellites immediately after confirming deployment of the new ones.
But yeah, you'd usually pay for service in a certain (large) geographic area, and if you wanted to take your pager out of that area while on a trip, or if you moved, you'd have to let the pager company know so they could start broadcasting in the new area.