What relevance does conventional musical theatre have to Hamilton? While he is undoubtedly steeped in rap, hip-hop and R&B music, Lin-Manuel Miranda also has a thorough foundation in musicals. (In fact, his wedding was even set to the music of “To Life” from Fiddler on the Roof.) Stephen Sondheim, who worked with Miranda on the 2009 revival of West Side Story says, “Lin-Manuel's use of rap is that he's got one foot in the past. He knows theatre. He respects and understands the value of good rhyming, without which the lines tend to flatten out.” 
In Hamilton, Miranda actually cites the 1969 Broadway historical hit 1776, quoting its opening number “Sit Down, John!” in reference to the same character, John Adams. He also cites Gilbert and Sullivan’s “The Modern Major General” from Pirates of Penzance, and was influenced by Sondheim’s Assassins (“a master class in, Okay, how are these people similar, how are they different, what do they want, what story are we telling in this one song?”) Jason Robert Browne’s The Last Five Years (“At the end of Hamilton’s affair with Maria Reynolds; he sings, ‘Nobody needs to know,’ and Jason wrote the ultimate infidelity jam called ‘Nobody Needs to Know.’ The moment I had the idea, I called Jason and was like, ‘Ahhhhh, I need to make this reference!’”) and Les Misérables (“I learned a lot from Les Miz about compression and returning to themes.”)
I am not going to try to speculate on what Hamilton’s influence will be – not since Clive Barnes infamously insisted that all post Hair musicals must be rock has anybody done something that misguided. Besides, so much of Hamilton is so specific to its subject that it is hard to imagine how anybody else could employ the same techniques (although I know we are going to be subjected to hundreds of would-be imitators). Sondheim says, “Hamilton is a breakthrough, but it doesn't exactly introduce a new era. Nothing introduces an era. What it does is empower people to think differently. There's always got to be an innovator, somebody who experiments first with new forms.”
However, what it most significant about Hamilton is not its music – much of which is not actually rap or hip-hop – or even its form, but its notion of inclusiveness. Its story of American history is told by a largely non-white cast using musical and theatrical forms that they are comfortable with but that would be anachronisms if taken literally. Many of the lyrics are narrative, making it at times more like an oratorio than a musical. Just as Stanley Kubrick achieved his stunning effects in 2001: A Space Odyssey by, in part, choosing only to do that which he could do very well, Miranda limits his use of rap and hip-hop to appropriate situations as a narrative device, often with humorous results. There is little in Hamilton that could be described as “naturalistic”. By doing this, he allows the audience to accept the notion that the story is being relayed through the media of “modern” people. Not only does it help modern audiences to accept it, but it also conveys the notion that they are, or at least can be a part of it.
He would not be able to do this had he not had a full musical and theatrical vocabulary. No one musical form – be it rock or ragtime – has the emotional range by itself to tell a great story. Just as Stephen Schwartz, a generation earlier combined his love of folk and Motown with his respect for the work of Leonard Bernstein and of Harnick and Bock, Miranda is a merger of two worlds. This is, and always has been, how the musical moves forward. Both the performers and the writers need to have a broad background. Study everything. Pop, classical, musical theatre – it all goes together into the great mix, but a musical, more than any other form, requires eclecticism.
I am still available as a lecturer on musical theatre, both as a visiting/guest lecturer or as a tutor.
 Michael Gioia, “Stephen Sondheim says Hamilton is a breakthrough”,Playbill, 8 July 2015 http://www.playbill.com/article/stephen-sondheim-says-hamilton-is-a-breakthrough-com-352907