It has a violent revolution. But your question contains an unstated assumption: that capitalism leads to "the majority of the citizenry [ending] up in the underclass". Feudal societies saw most people living in poverty. Communist societies saw most people living in poverty. Properly functioning capitalist societies have a healthy middle class, and a tolerable standard of living even for people at the bottom.
"So you can pontificate about the ideological merits of extreme Libertarianism all you want, but in practice it works exactly as well as extreme socialism."
The society that came closest to "extreme Libertarianism" was the United States in the 19th century. (Especially after the civil war). That was the century of the industrial revolution, huge advances in technology and wealth production, and an unprecedented rise in the standard of living.
