Well, some musicians arguably have. Think about the historical significance of The Beatles, for example. As for Green Day, I suppose whether or not that's something you can write is really going to depend on how well you can make your point. You could talk about Green Day being one of the most well-known and influential bands in the era of protest music against George W. Bush and the Iraq War. I don't think that era of music is nearly as significant as Vietnam War time, but I think it'll be historically remembered.
If you want to write an essay in a three-point style (which I hate personally because it's so goddamn generic and boring, but high school teachers will always give you an A for one that's well done), try to structure it like this: Talk briefly about Green Day's early history. Mention "Dookie" as helping shape the trend of 90's pop-punk but don't spend a lot of time on it. Talk about the success of American Idiot in 2004, transition into the whole protest music theme. The lyrics of American Idiot and Holiday, the WMUWSE video, the Bullet in a Bible show. Throw in a few quotes, like when Billie introduced Holiday on stage with "this song is not anti-American, this song is anti-war!" Give a shout out to a few other artists who were part of this trend (like Eminem with his song "Mosh"). Then the third and last part can be about how unique and innovative the American Idiot broadway show was. Its success as a sung-through musical and all.
Be creative. Try to relate it to your generation. There are literally dozens of lyrics you could just pull out of the top of your head, "class of '13", "steady diet of soda pop and Ritalin", say that Green Day relates to how a lot of kids your age feel lost and without a place or identity. Sum it up with that.