Interesting discussion at Broadwayworld.com on whether "Light in the Piazza" is a musical or "a play with music." The answer seems to be yes, it is a musical, though perhaps a "chamber musical." There is some suggestion of a gap between the songs and the story--which could explain why it won so many Tonys but not "best musical." In addition, the question is raised whether a "musical," to fit the bill, has to be a musical comedy, preferably with dancing.
Adam Guettel's concern from the beginning (we've heard) was that the production would be a bit too precious, refined, subtle, or something to make it on Broadway. That's why he went on the regional circuit first--to test it, to build it up. It was a good move.
Reviewing the Chicago production for the New Yorker last year, John Lahr practically dared Broadway to take it on: "'The Light in the Piazza' doesn’t want to make theatregoers feel good; it wants to make them feel deeply. This it does, and that is why, despite the show’s quality, I suspect that the swamis of the rialto will pass on bringing it to Broadway. Still, Guettel’s kind of talent cannot be denied. He shouldn’t change for Broadway; Broadway, if it is to survive as a creative theatrical force, should change for him."