What, exactly, is the purpose of government?

From Aretae:

Because the interests of the elite do not match the interests of the whole of society, the natural flow of governance is for elites to aggregate ever more power, and the populace to become ever more immiserated....

The depressingly elegant thing about this is that the game theory is stable. Take the folks who make decisions, build as small a stable coalition as you can, and divide the spoils among the small coalition. It's as inexorable a solution as gravity, given power politics.

This is what governments do when they can. The core challenge of government is how to prevent that.