I think that this is extremely simplistic. For example it does not account for individualist anarchism or the collectivist "for our country/nation/race" pushed by various fascist governments.
I can't see how "doesn't cover absolutely all corner cases" equals "extremely simplistic". I'm fairly sure that in broad terms, "left / right" covers the political spectrum the absolute majority of people inhabit. Your objection feels like futile quibbling to me.
