Why can't I play my radio's phono output through my

(Should have specified: *through the stereo audio channels of my TV's component input)

I'd think the same thing about the video signal, but really you should get sound. Try another amp, or give it a video signal just to test like from a VCR etc

at least some modern tvs will mute the audio unless there's a video signal available on that input
also, of course, ensure the tv is on the correct input

phono needs an amp.