The Eagles songs survived all through the 80s when they weren't touring because of radio airplay. Listening to the lyrics, I can see what you mean about "Island Girl" not being PC, and I can see why it wouldn't get aired out much today onstage or on the radio. As for the others, I don't listen to radio as much now, but I listened to classic rock radio a lot back in the day. The radio station I listened to played several of those artists a lot - just not those particular songs.
Interestingly, the songs that I have heard from the list, the ones that got played a lot on my radio station, are actually toward the bottom of that list: "S.O.S.", "That's the Way I Like It," "Born to Run," "Saturday Night" (Bay City Rollers), and "Dance With Me." (I never heard "Keep on Tryin'" until I got into the Eagles.)