I'm not at all convinced by the Pinochet miracle.
There's not much difference between "disappearing" your political enemies and "disappearing" small business owners, wealthy, successful entrepreneurs, etc. All it takes is a dictator who can't see the difference and your lassiez-faire state is suddenly bankrupt. First they came for the communists...
The only reason Pinochet "worked" was he followed Chicago to the letter. Any system can work, for a time, as long as you follow its core principles strictly and remove outside interference. But would a Pinochet economy survive a 2008-style recession? Would a Pinochet economy survive threat of invasion, or external interference, or a global war? Probably not. And of course in the end it didn't work. He's gone and his regime is gone.
Fuhrerprinzip is probably more stable than Pinochet, because it creates a cult of personality. It didn't work under Hitler, because of his personality of pitting one person against another person and having duplication of the same level of authority. But imagine Fuhrerprinzip under someone like Stalin (obsessive micromanager rather than hands-off idealist) and it can be long term stable. Something like North Korea (god worship) would be "stable". With a low quality of living of course, but that's the price of not being a modern liberal democracy.