LexBaird 'eliminating laws on drugs or abortion, both of which lessen the authority of the State'
That is of the Libertarian ideology
LexBaird 'but at a cost to society.'
Having the government pay for it is of the Leftist - Socialist ideology at the other end of the scale
Two separate ideologies, two Different points on the lineal model.
And there you are using a second logical fallacy: begging the question.
It goes like this: “since I am defining the terms as me being correct, I am therefore correct. Thus the question is resolved in the premise.”
Your premise is incorrect because your definitions are too limited, as leftist/rightist and statist/anarchist are not the same line. You model is too simplistic to account for variations, such as absolute monarchy or theocracy (right-wing statist) or revolutionary anarchist (left-wing anti-statist).