Radio 4 is primarily spoken word - you're not going to hear much music of any genre. If you want to hear music, listen to music stations.

What is the difference between a poetry-lover wanting to hear a particular poem read aloud (a different experience from reading it oneself) and a music-lover requesting a song?

Plenty of people would wonder why anyone would pay good money to go to a folk club. I don't understand why anyone would pay good money to go to a football match, or to watch golf. It's just a matter of taste, because you don't enjoy something yourself doesn't make those who do 'wallies'. You appear to have a bit of a chip on your shoulder.