To answer your question about All American:
I did a little bit of internet sleuthing, and it appears that All American had a bit of a turbulent development process. It's book is credited to Mel Brooks, of all people, who never finished the second act (it was 1962, so he was presumably busy with The 2000 Year Old Man and Get Smart), and it was handed off to Joshua Logan, who also directed the Broadway production. Logan had a wildly different writing style than Brooks, and he was also starting to suffer from bipolar disorder, so the book was kind of a mess and the show flopped. The version licensed by Dramatic Publishing Company (the version I'm assuming you read, adds another writing credit, June Walker Rogers, a Broadway dancer-turned-writer (who coincidentally passed away back in July). Presumably, she did a rewrite of the original script to meld the original two visions, and make it more suitable for licensing and production, which is what you read.
To answer your broader question of when/why published scripts to musicals are different than their Broadway versions, it happens often, for several reasons. Many shows have significant rewrites between Broadway and the National Tour (modern examples of this include Shrek, Mean Girls, and The Addams Family), either to better suit a production that's on the road, or possibly because the writers wanted to take another stab at the material. There are also "high school" versions of shows, that may cut technically challenging songs, rewrite scenes to be age-appropriate, or transpose keys to suit younger voices. (MTI has a huge library of high school, TYA, and Jr. titles). Finally, older, outdated shows may be rewritten, either by the original writers or by new ones (as in the case of All American) to better suit modern sensibilities. This may be to change aspects that are now seen as politically incorrect, or they may be to flesh out the plot to meet modern audience expectations (books for musicals used to just be excuses for songs to occur, there wasn't much thought put into dramatic structure).
Nevertheless, it's an interesting and exciting world, and looking at the scripts for musicals that you can't experience through watching or doing is something I wished more people did. There's a world of phenomenal shows that don't get performed anymore for any number of reasons, and fade into the ether if it weren't for the published scripts being discovered again.