You can ertainly encompass more complexity on two axes than on one axis, but the problem with your approach is that someone else will then add a third and fourth axis to your model, sacrificing simplicity for an always insufficiently complex model. The world as too complex for any number of axes to plot reality.

In the interests of simplicity, I shall stick with my model where Right is the pole of freedom, especially freedom of speech, and of lassez-faire free market Capitalism. As you say, the extreme right is libertarian anarchy, but I favour Government just big enough to enforce ethical behaviour on Business.

The Left is progessively more Authoritarian from Democratic Socialist to Communist, a spectrum of Big Government, Tax and spending increases, wealth redistribution tending towards Nationalising everything and running a State economy the worst possible way: Central Planning by State Bureaucrats. Communists and Socialists are different only in degree: in a democratic system Socialists do not have absolute power, and must moderate their behaviour to be re-elected. A Communist is simply a Socialist with absolute power and no limits imposed on their ideology.

For most purposes one axis of Left and Right is enough to define the debate.