I thought Saints Row IV and Sleeping Dogs did this really well, to the point where I'd go around in the car just to hear all the radio stations.
Kinda but not really. The music was all created for the game specifically, this wasn’t a GTA situation. It contributes a lot to the weird atmosphere of that game, hence me being flabbergasted he rolled credits on it having no clue it was there.
My experience playing the first few areas/levels was frequent, unskippable radio chatter telling me to do things when all I wanted was to be alone and explore the weirdness. I didn't (yet?) find out about the music stations but would probably avoid them and the game had my full attention.