Once Upon A Time is from the 1962 musical All American by Charles Strouse and Lee Adams, the authors of Bye Bye Birdie, Golden Boy and Applause.  Strouse also wrote Annie with Martin Charnin.  So, with that pedigree, how come All American (which also featured a book by Mel Brooks) failed so utterly?  A glance at the plot (courtesy of Wikipedia) may provide some explanation:

Based on the Robert Lewis Taylor 1950 novel Professor Fodorski, it is set on the campus of the fictional Southern Baptist Institute of Technology where the worlds of science and sports collide when the principles of engineering are applied to football strategies, and football strategies are used to teach the principles of engineering.  The techniques of a Hungarian immigrant, Professor Fodorski, prove to be successful, resulting in a winning team, and he finds himself the target of a Madison Avenue ad man who wants to exploit his new-found fame.

Hmmm.

Tony Bennett recorded the song on his ...San Francisco album thereby rescuing it from obscurity - and subsequent versions by Frank Sinatra and Jack Jones helped to assure its place as a minor standard.  If anyone can find Moira Anderson’s version (I kid you not) please let me know.

As well as possessing one of the most beautiful and technically perfect voices in the business, Maureen McGovern has recorded more film themes than any one woman should have to (look ‘em up, youngsters).  She’s also appeared on Broadway and recorded CDs dedicated to Gershwin and Arlen as well as two duet albums with pianist Mike Renzi.  This is from the second, The Pleasure Of His Company