I'd argue that the broken society narrative is a subjective opinion and not objectively quantfiable. One man's broken society is another man's utopia, it's all dependent on your personal beliefs.
Its probably as dependent on your position in such a society.
I think there are some measures you can use to say some aspects of society are more broken than in the past, for instance suicide[1].
Steven Pinker's latest book, "Enlightenment Now", has a pretty good treatment on suicide rates and other "broken-ness" indicators. The data-driven conclusion is that on almost every metric civilization is less broken than before, if it could indeed be called broken at all.