As Charles Strouse will tell anyone who will listen, "Bye Bye Birdie" was the first rock musical.
We did it my senior year of high school and I've seen many productions over the years. In my evolving understanding of such things, I now get that "Birdie" was the "Book of Mormon" of it's time (though much more American-universal). "Birdie" was (for then) very modern satire of the times it was set, farcically commenting on the era's casual racism, it's burgeoning worship of celebrity culture and the new power of the teenager. "Hymn For A Sunday Evening" was so late 50's/early 60's culturally specific, just as "Mormon's" references are so of the moment. Though possibly eye-rolling now, "How Lovely To Be a Woman" was theatrical irony playing out in one number, very smart for the time. (And though no feminist icon, Kim is smart enough to eventually realize kissing an older man isn't exactly the way to grow up and balks at the idea).
I also believe that the show doesn't work well anymore because it is always revived sincerely. I'm thinking a truly innovative director could take that original satire and take it to it's extreme, not exactly a "wink-wink" revival, but maybe in that direction.