Ham radio operator and electrical engineer here.
There are multiple reasons.
1) TV transmitters tended to cover a large area and any radio signal weakens by the cube of the distance. FM radio tends to be more local.
2) video uses AM modulation which is more affected by interference and atmospheric events. The stronger the signal, the better the quality. FM tends to be full quality until you reach a threshold, then it is gone.
3) Buildings block a lot of signal. An FM radio antenna on a car works well. It works fine inside if you are somewhat near a transmitter. If you were able to put “rabbit ears” on top of a building, you would likely get much better TV reception.
It’s analogous to attending a concert at a large arena. Your ears work just fine to hear the music because there are really loud speakers. You may even feel overwhelmed because the sound is so loud and inescapable. Maybe it’s a bit echoey, but the music is clearly recognizable enough to be enjoyable. If you want to watch the performance, though, you have to actually look at the stage. Maybe that’s hard to do because there are people standing in front of you. Maybe you bought lawn seats, and the performers might as well be ants. If you were clever, you brought binoculars.
An FM modulated audio signal, like sound, can reflect all over the place. Like your ears and your brain, it’s easy for an FM radio to pick it up that signal with a simple antenna and convert it to recognizable music, even if there’s a bunch of background noise and echos.
An AM modulated video signal, like light, also reflects all over the place. Like binoculars with your eyes, your TV needs a directional antenna with a clear line-of-sight to the transmitter in order for the signal to be converted to a recognizable image.
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