I gave up the “Left<>Right” model some years ago, as I believe the “Total Control<>Anarchy” model is a more accurate and descriptive one.
It bunches Communism and Fascism at one end (Total Control, which is undesirable) and puts Anarchy (total lack of control or protection at the other)
The optimal solution is somewhere on the continuum between those two, which I think is consistent with our current form of big “C” Conservatism. Where, exactly, is still contentious with the Libertarians tending towards the side of Anarchy, and the Leftists tending towards total control.
That is an interesting “Challenge” you pose. I’m going to think on that.