I think not too many would understand the left-right dichotomy that way. We do not have to consider the Nazis to highlight that. Conservatives are generally considered right wing, yet in terms of individual freedom you would end up classifying them as left wing. It is in those quarters that one typically finds opposition against such things as gay marriage, abortion, legalization of drugs and while they are usually not against the free market, they are not ideologically or practically committed to it either. It seems to me that in your dichotomy, you'd find anarchists on one side and everybody else on the other. While that is not an invalid dimension (see the political compass) it is at the very least confusing to re-define that axis as the left-right one (and what remains of the traditional left right one?).