Patrick Healy discusses an important aspect of what gets to play on Broadway…the shortage of (and therefore, competition for) theaters. Some shows don't reach the Great White Way because, quite simply, there's no suitable house available when they need it.
There are all sorts of stories about this kind of thing. Richard Sherman told me that the stage version of Chitty Chitty Bang Bang only got to Broadway because the revival of 42nd Street closed at the Hilton Theater. There were only one or two houses that could accommodate the special effects necessary for the show's flying car and the rest were booked solid, probably for years to come.
All sorts of shows are aspiring to make it to New York in the next year or two. Just in the musical category, we have revivals of How to Succeed, Brigadoon, Godspell, Dirty Dancing and Fosse's Dancin' and new musicals adapting Betty Boop, Spider-Man, Paradise Lost, the life of Bruce Lee, the life of Harry Houdini, and the life of Liberace, as well as a number of movies including Catch Me If You Can, Father of the Bride, Robin and the Seven Hoods, Pure Country, Priscilla Queen of the Desert, Leap of Faith and the Jerry Lewis masterpiece, The Nutty Professor. There are at least thirty other plays or original musicals that have announced an intention to play Broadway. There can never possibly be enough theaters for half of them.