That a bad liberal democracy doesn't exist shouldn't surprise us, since, if it was bad, we wouldn't consider it liberal.
The "liberal" in liberal democracy stands for classical liberalism, not "liberalism" in the US sense. Moldbug's philosophy is consistent with classical liberalism; when he talks about "liberalism" being a bad thing, he means the US modern sense.
IOW, the fact that "authoritarian democracies" exist at all, and are even common in "transitioning", "democratizing" countries without a strong historical legacy, would seem to argue for Moldbug's point. For comparison, consider countries such as Singapore and South Korea; the latter successfully transitioned from a non-democratic regime which did nonetheless uphold liberal principles and individual rights to a modern liberal democracy. Japan is also an interesting case, although its involvement in WWII makes things unclear. Nonetheless, the Tokugawa-Meiji-Taishou periods did involve increasing recognition of individual rights.
The "liberal" in liberal democracy stands for classical liberalism, not "liberalism" in the US sense.
Classical liberalism is often identified with libertarianism so I just want to emphasize that the "liberal democracy" refers to liberalism in a generic, John Stuart Mill, sense. From wikipedia:
...It is characterized by fair, free, and competitive elections between multiple distinct political parties, a separation of powers into different branches of government, the rule of law in everyday life as part of an open society, and
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.