What does VFR operations have to do with it? This is not a distinction
made by the regulations (if I'm wrong, please cite the reg).
You're wrong, I'll cite the regulation for you again:

§ 91.129 Operations in Class D airspace.
[snip]
The regulation requires two-way radio communications to be established with
*the* ATC facility providing air traffic services prior to entering that
airspace. It's specific, it doesn't say *an* ATC facility providing
services.

Nothing there says anything about IFR or VFR. As for =the= ATC
facility, there is no distinction in the regs that pilots are presumed
to be familiar with for through flights vs terminating flights.

I see your point:
The radar controller can coordinate flights through Class D
airspace with the tower but flights that are landing at the towered field
must be shipped to the tower prior to entering Class D airspace.

After all, the tower's specific authority is over the runways, not over
over the runways, and this would require communication with the actual
tower if one is landing there. But 91.129 says "with the ATC facility
([...]) providing air traffic services", and this doesn't (as you state
above) require it to be the tower, if there is some letter of agreement
that some other ATC facility will provide the services. Pilots are not
expected to be aware of all the letters of agreement, are they?

Jose
--
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