I think of the radio similar to television. For example, I can have any tv show and movie at my finger tips, but sometimes it's nice just to turn on the tv. There's something enjoyable about letting someone else make the choice. It's the same reason you might have a DVD library collecting dust, but you get excited when one of your DVD's appears on television. You just push a button, no decision of which movie to watch, and no taking time to setup a DVD.
It's similar with the radio. Any song or album is available online, but sometimes I just want to listen to music, without finding a new playlist every hour, or switching songs constantly. Music streaming services online have this covered to some extent, but there's something comforting about a box that's sole purpose is to play music, and that's where the radio comes in.
Imagine if you had a box next to you, and all it had was a volume knob and 8 buttons, each for a different genre of music. You push classic rock, and it just starts playing a non-stop stream. Get bored with it? Switch to electronic. Your only choice is which genre, and how loud. No sign-up, no advertisements, no accounts to manage, no downtime, no social media, etc.