I'm enjoying the discussion/evisceration.
1959 is a bit too late to be considered mid-fifties, but FWIW, Sinatra's Come Dance With Me included several songs from roughly contemporaneous Broadway shows: "Just in Time," "Baubles, Bangles and Beads," "Too Close for Comfort," and "I Could Have Danced All Night."
(One can suppose the selection was quite conscious, that Sinatra, or somebody, said, "Hey, why don't we do some of the newer Broadway stuff for a change?")