A couple of questions and comments: I assume breakdowns are the book writer's description of each character at the beginning of the book. Is that what people are referring to?
I can see why someone who doesn't match the breakdown wants to play the role. If he or she is a big enough star, the individual might succeed in getting a shot, such as Mary Tyler Moore playing the previously male lead role in "Whose Life is it Anyway?"
I hope that white people don't usually want to grab the few lead roles available for African American performers. However, if the role is meaty enough, and the CHARACTER can be white (which we know, of course, that Hamilton, Jefferson, George Washington, and the others were), I could see someone's falling in love with the role and saying, "I really want to play that role -- it's perfect for my acting skills and my voice." Is that selfish? Maybe, but the theatre is an inherently competitive profession.
As far as Galinda's being played by an African-American performer, Galinda's casting has been so rigid that I doubt a white woman with brown hair and brown eyes would be selected; part of the joke about Galinda's being "Miss Perfection" is probably that she has to look like the epitome of Aryan womanhood. That wink at the audience would have gotten lost if Idina Menzel or Audra McDonald had been cast as the first Galinda.
As I've said many times, white characters can easily be played by nonwhite performers as long as people understand that the character is white even if the actor isn't -- we're seeing that now with Hamilton. To me, the trickier question is deciding when the CHARACTER needs to be white even though the performer is not. Christine Daae can easily be played by an African-American performer. It would take only a tiny bit of tweaking -- a line saying that she is the daughter of the Swedish violinist and a singer from Algeria. As for white characters, Hamilton is one example. Yitzchak in Hedwig, Tevye in Fiddler, Freddy in My Fair Lady, and Raoul in POTO are white characters, and probably can't be tweaked to make them anything else. Yet, that doesn't mean that a person of color can't play the roles (e.g., Rebecca Jones as Yitzie).
The conversations about race on this board are long overdue in the United States in general. There are certainly lots of racists in North America and Europe, but I doubt that too many of them hang around with theatre people, who are generally an accepting group of folks.
Happy New Year!
Audrey Liebross
Audrey, the Phantom Phanatic, who nonetheless would rather be Jean Valjean, who knew how to make lemonade out of lemons.