In the book, he makes the compelling case that complex societies are, at root, very successful problem solving systems. If they weren't, they would never have become complex in the first place. Why? Societies solve challenges by creating new rules and processes (new complexity) that are then added on to the existing system ad infinitum. More successful outcomes = more complexity.
However, as noted above, problem solving comes at a cost. Each solution leaves a residue, a layer of complexity that never goes away (laws, taxes, monopolies, treaties, etc.). It builds up over time and saps the social system's flexibility and efficiency. Eventually, ever new layer of complexity extracts more in costs than it provides in benefit (solution). At that point, according to Tainter's analysis of ancient civilizations, the complex society collapses.
What if the complexity is not the nation-state or enterprise but humanity? There are very few system or total collapses (world war, dark ages) on a macro-level (time and scale), I am not sure that the view of collapse holds. The human network is on one path toward global complexity. We progress but are rooted in basic human needs and requirements.
And yet. I love the logic and feel this riff has at kicking dust in the eyes of the giant old dinosaurs.