A true absence of power will create a vacuum, something will rush in to fill it. If not some new government constituted primarily to benefit its rulers, then some alliance of gangsters or businessmen whose "competition" will not moderate the tyranny, but just involve everyone else in the bloody conflict that determines the head bully.

When the Empire falls, you don't get a Libertarian paradise, you get feudalism, serfs, warlords, local barons, fiefdoms and constant war as the bosses jockey for power. Every culture with a feudal past went through the same process, in Europe, China, and Japan. When the Emperor lost his grip, the power was taken over by those who were able to monopolize the means of production (generally, in those days, agriculture). And feudalism, although relatively stable, is not a meritocracy, although the thugs in charge tend to feel it is because they are convinced they have god-given merit due to their superior cunning, strength, brutality, or entrepreneurial skills.

The Libertarian Utopia will be a corporate medievalism, with the world divided into industrial monopolies, great plantations, and street gang turf.