Hmm I am not sure I fully agree with you...
You look at the "left" and the "right" in terms of a rather... social aspect. Yes you mentioned that extreme right wing believes in social inequality as well as some other type of "market" inequality as well but I am not sure that is the proper way to describe either party. Equality in terms of the people makes a little bit of sense. A liberal society would want to be a smaller gap in classes than say a conservative society, but each are trying to remove social classes. An extreme liberal would remove both rich and poor classes while inevitably an extreme conservative would remove a middle class.
Even in some social issues I suppose there may be some type of natural inequality in the social system of America now, but personally I blame that far more on the liberal left-wingers than the right. Maybe originally it wasn't so but nowadays a person can't say black or gay without heads turning, yet the term cracker is never censored in media like other racial slurs. This is the only real social inequality I see in America, on a whole.
The politics these days I think are less viewed in terms of an "equality" sense as really it comes down to issues with government. Less of a left and right thing but more of an up and down thing I suppose. Governmental politics are so very control centered that I think both drown out what you would consider to be the determining factor in what makes left or right. It isn't that the US is a country full of right-centrists and right-wingers as much as the illusion is within there being a color at all. There is no red and blue, just a government that ultimately wants to control the people.
I guess where I disagree with you is that I think the left and right in terms of equality should be looked at it in eyes of the government. Left wing to me is the government keeping everyone on equal disadvantage with the government. The leftists are ok with this decision of "equality" because even though personal freedoms are watered down it keeps a feeling of safety. Right wing to me, is when the people don't accept this and oppose the government forcing the people to be regulated into being the same person as everyone else.
edit on 10-1-2013 by PhysicsAdept because: (no reason given)