I think it's true that no GREAT show ever failed to make it to Broadway because the star dropped out, but there are plenty of examples of so-so shows and star vehicles that were scheduled to open on Broadway were cancelled when the star got sick, hurt, died or was otherwise indisposed prior to the opening.
One example was Kander & Ebb's THE VISIT which was slated to go to Broadway until Angela Lansbury dropped out to take care of her ailing husband (who eventually died). It's been done regionally since then (at least once with Chita Rivera in the lead), but I don't think there have been any serious efforts to move it to New York since Lansbury opted not to do it.
I also wonder if Laurents' JOLSON SINGS AGAIN would have ever actually made it to Broadway had LuPone not dropped out of it (as he has claimed it would have), but since no other major name has been willing to do it, it's remained in regional houses.
I suppose one could also include BUSKER ALLEY in this as well. Not that the show would have ever been a big hit, but it was scheduled to move to Broadway until Tune broke his ankle on that lamppost on the pre-Broadway tour. When no suitable replacement could be found, the production shut down.
I think Ken Mandelbaum has a few other examples of shows that closed out of town when the star became indisposed and no suitable replacement star could be found in time in his book NOT SINCE CARRIE.
"What a story........ everything but the bloodhounds snappin' at her rear end." -- Birdie
[http://margochanning.broadwayworld.com/]
"The Devil Be Hittin' Me" -- Whitney