How about the late 50s. 4 years ago, Chuck Berry and Fats Domino died. After Little Richard died 1 year ago, I read that there were 2 greats left from the 50s, Don Everly and Jerry Lee Lewis. Since Saturday, it's been just Jerry Lee. In chronological order from 1957-62: Bye Bye Love Wake Up Little Susie All I Have to Do is Dream Bird Dog Problems Devoted to You (Till) I Kissed You Cathy’s Clown So Sad Walk Right Back Crying in the Rain If you toted around your new-fangled transistor radio, no vacuum tubes anymore, in the 60s, 70s, and oldies radio in the 80s, every rock & roll station played one of those 11 songs like, every hour.
I had a one transistor radio back in the early 60s. However, some of those songs you listed came well before the one transistor radio.
Yes, 1957 was a little too early. I still have my Sony from about 1962, in its removable cover. It probably still works, unless it contains a decayed battery. No moving parts. This is the first time in 50 years that it has occurred to me to look at it and turn it on.
Before that, when I was a tiny tike, I had a radio that had no batteries and used no power. I used to use our iron bed frame as an antenna which I would attach to my little crystal radio by an alligator clip. There was enough juice in the airwaves to produce an audible sound in my tiny ear bud.
I tried to build one when I was in the Boy Scouts. It employed a "Cat's Whisker" as a diode and a crystal for tuning. I never could do it, though. The one I used was commercially made and it's internals were encased in a red and white plastic rocket ship and I had it before going into the Boy Scouts.