In direct democracy with most important decisions being taken directly by voters, there's no selection process - so they will be as unsuccessful as dictatorships. This is extremely surprising prediction to me, but remarkably bad economic performance of California seems to confirm this.

I'm gonna go ahead and call confirmation bias on this one. You might be right, but I think we need more clearly defined metrics of "success" and a larger sample to draw sensible conclusions here; not just the first confirmatory example that comes to mind. Switzerland has a fair amount of direct democracy, and its extent varies between cantons. Maybe that could provide a useful test?

(Does ancient Greece count, or was the franchise too restricted?)

Nitpick: Do you reckon you could clean up that introductory sentence? I had to read it at least three times before I could parse it.