I've taught in a number of high schools, and history and the role of government has always been taught in social studies classes. I'm not sure what more this opinion piece is suggesting. My guess is that any effort to teach the responsibilities of each citizen--other than really generic things like vote and obey the laws--will result in bitter, local political feuds. Schools don't need that.
I would like to see History classes require more independent reading of their students. There is such a wealth of reading available now, and easily available with e-readers--biographies, memoirs, even historical fiction--that students will acquire a much more nuanced sense of what being a citizen means than can ever be taught in a classroom.