What makes it “technically” not a cover? I thought a cover was any song not composed by the performer, and made famous by someone else.
OK. I accept your correction.
By that logic, I think we can include “Pinball Wizard”, which made #4 in the UK on its initial release in 1969, which 24 years later was incorporated into the Broadway adaptation of Tommy.
“Put On a Happy Face” from Bye Bye Birdie was a pretty big jazz hit for Oscar Peterson in 1961. It probably didn’t chart on the Billboard Top 100, but I’m not sure that’s the standard we’re going for here. I think Julie Andrews’ “My Favorite Things” from My Fair Lady got some serious airplay. Ditto “You’re the Top” from Anything Goes. “Night and Day,” also by Cole Porter?
Doesn’t need to be made famous by someone else does it? Just anyone but the original artist performing the song is called a ‘cover’.
The Sound of Music
…whereas “On the Street Where You Live” was a hit from My Fair Lady.
(No.4 on Billboard and no.1 in the UK for Vic Damone)
Shirley Bassey’s recording of “Big Spender” from Sweet Charity was a Top 40 hit in the UK.
How far back do you want to go?
After all the musicals from the 20s onward produced a large body of standards from Cole Porter, Gershwin, Jerome Kern, Rodgers and Hart… etc etc.
Maybe not so many of those became actual stand-alone radio ‘hits’, but they are certainly played on radio to this day, though not performed by the original theater artists of course…
“Ease On Down The Road,” from The Wiz.
“The Impossible Dream (The Quest)” from Man of La Mancha
“Who Can I Turn To?” from The Roar of the Greasepaint - The Smell of the Crowd has reached the charts in several versions, most famously the 1964 recording by Tony Bennett.
“If Ever I Would Leave You” from Camelot.
(It’s only a model.)
This. My answer to this question is Cohan’s Give My Regards to Broadway which may never have been a ‘radio hit’, but is definitely a well-known song.