> I am also confused by cliffs. Maybe someone more knowledgeable than me could explain why you would ever want them for something like this instead of just having higher progressive tax rates for well off people

Because middle-income clawback with sharp cliffs rather than gradual clawback starting or reaching into upper income ranges pits the middle-income segment of the working class against the poor in funding battles, helping to avoid political pressure to further increase benefits, and it also allows what can be marketed as a support system for the poor to also serve as an anchor that creates a progress wall just above the area where it provides net benefits, while minimizing the marginal impact on high-income earners.

Is this socially good? No. But it serves the interests of the people who politicians tend to see as their most important constituents, while creating a sharp division of interests between the poor and middle-income segments of the working class, obstructing the formation of working-class solidarity.