This has basically be my thing for the past many years now. I don't mind listening to the radio, but even our alternative rock plays the same 20 songs, but then a few other older but still super popular songs. I know my GF who listens to a ton of that alternative and alt 90's rock thinks that there is something wrong with me or I am just trying to be a hipster, but she also doesn't listen to as much music as I do, and she is the type of person who cherry picks songs from an artist but never look into anymore music by that artist. I am not saying that makes her a bad person because I get that is the way that most people listen to music, but I enjoy listening to an entire album as an experience and if I like that album, look into their other stuff.
I listen to a bunch of the college stations and they actually play new music, but will also play some of the deeper cuts from really old classic rock for like a 2 hour block during one night a week. You will never hear Stairway to Heaven, Iron Man, or Barracuda anywhere in there. I like this and continue to listen, and even a year ago when I could threw a few bucks their way during their donation drive.
You are exactly like me. I can't cherry pick songs. I always delve deeper and listen to albums at a time. I end up licking the entire library of an artist most of the time, and the closest thing to cherry picking would be liking a single entire album of some particular artist.