This musical failed because no one asked a basic question that needs to be asked when an idea is first proposed. "What do these people have to sing about?"
The characters in Sweet Smell of Success have nothing to sing about. They are about as non-musical as they come.
Gower Champion had a rule of musical theatre. "Who do you root for?" In Sweet Smell the answer is no one.
Rent the movie which is nasty, sharp, mean-spirited and damn good.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher