"great society" is not being used a rhetorical device to refer to a particular society; it is (I am reasonably sure) referring to the "Great Society" program in the United States [0] in the mid-60s. I don't know enough to address the claims in the GP, but they did frame their argument, at least.

[0] https://en.wikipedia.org/wiki/Great_Society

The "Great Society" was Lyndon Johnson's domestic legislative program.

It created the framework for how social services are delivered.