(And these aren't remote/unpopulated areas: you can find plenty of satellite dead zones 2-3 hours outside of NYC in the Catskills.)
Yes, I agree that satellite coverage is not 100%. But neither is radio.
I've had the same experience as you around remote places, but those places were generally the flat-and-desolate kind :-)
It's the radio stations who are in charge of situating their reception equipment where it can see the sat, and also for figuring out how to best broadcast to their served area (e.g. AM and/or FM? Tower height, power, setting up some translator stations on a different frequency to serve outlying areas, giving the feed to local cable systems to be sent with TV service, etc.)
I remember this being quite an issue trying to target geosync broadcast satellites like DirectTV/Dish. Even being in the shadow of a relatively small hill could block access if your location and local topology happened to create an unfortunate alignment. I've naively assumed Starlink's rotating constellation of thousands of LEO satellites reduces how often this is an issue - but maybe it doesn't?