"I think something else that makes it interesting is that most of the show is delivered straight out to the audience. The creators used the device of having the director at the back of the theater, and for most of the show, just a disembodied voice, which forced the actors on stage to look straight out into the theater, breaking the fourth wall."
Musicals have been doing that since THE BLACK CROOK, Goth. If there was a difference in A CHORUS LINE it was that they didn't pretend to be talking to each other.
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To the OP, I think ACL was important because it was so brilliantly staged and performed, but also because it dealt seriously with subjects that hadn't been well-covered by Broadway musicals before. The treatment of the homosexual, Paul, is (a) compassionate if sort of condescending to us now and (b) unusual because he wasn't the only gay character in the show. He was also not just gay, but has worked as a seedy drag queen, much to the shame of his parents.
And ACL acknowledged that not everybody can realize his/her dreams all the time. Only a minority of the dancers make the cut and we know from the beginning that most will be disappointed. ACL wasn't the first musical to have unhappy endings, but it may have been the first to have so many. As such it celebrated American aspirations while acknowledging limitations in a decade in which a President of the U.S. resigned, we lost our first war in Vietnam and Americans in general were cutting back because of oil embargoes and inflation.
There is no central love story or supporting, comic love story, both standard in the American musical since OKLAHOMA! There are no stock characters that one recognized from every other musical of the R&H period. And by using the dialogue and problems of real people, it had a ring of authenticity that contrasted sharply with the book librettos based in vaudeville routines that had dominated Broadway for most of the century. I wouldn't call it "gritty", but at the time it seemed a lot more "real" than something like APPLAUSE.
Yet it's overall tone was determined and even inspiring. "What I Did for Love" may be cheesy, but it also reflected the love and dedication of artists for their craft. The characters aren't trying to be stars (as the chorines of Busby Berkeley had been in the 1930s), they were just trying to be serious dancers. It was easy to root for that.