The California system has actually caused me to think more critically of direct democracy (see below). But it depends on how direct it is. People are too busy to conceivably craft informed legislation on countless complicated issues and it's simply more feasible to have full-time representatives for this purpose. This is true for an electorate of any size. I don't want to vote on tedious, difficult, wordy, and seemingly trivial ballot measures. Instead, I want to vote for qualified people who share my political orientation to do that stuff full-time on my behalf.
On the specific topic of the California system, I don't think it should be viewed as a model. This isn't just because it's resulted in a few bad propositions (prop 13 and prop 8 for instance), but because the system isn't terribly useful to begin with. Most propositions are ridiculous and, once approved, become difficult to get rid of. Consider that most ballot measures become enshrined in the California constitution. In the American model I'm familiar with, having a constitution that's difficult to modify is generally a good thing. But when the constitution engenders a massive range of issues, it stops making sense. In the most recent election, we had narrow issues involving kidney dialysis clinics (regulating how much clinics should refund patients given such and such conditions in such and such situations), whether private ambulance employees should be on-call when taking a break, and how much space chickens get before being slaughtered. Before that, we had condoms in porn, eliminating bilingual clases, horse meat, and in the 60s voters even banned cable TV (courts shot this down). None of these things are the kinds of critical issues that should be part of a state constitution. Maybe that's just my idea of what a constitution should entail, but consider that these things are difficult to eliminate once passed. Take prop 13. It's universally reviled by all but a few lucky landlords and yet somehow we're still stuck with it 40 years later. Because any ballot measure is something we might have to live with for decades, they should be important. And yet they're usually random and narrow issues the average voter never even thinks about (which actually leads a larger criticism of direct democracy I'll get to in a sec). These relatively unimportant issues aren't things voters should be tasked to decide. Instead, we generally have full-time elected representatives for this. These represenatives are the ones who should do the deep-dive into regulating kidney dialysis clinics and studying STD transmission rates associated condomless porn. More importantly, issues that pass through the legislature don't have the permanent status that accompany ballot measures. And they similarly don't tie up the legislature with a labyrinth of impregnable funding/legal restrictions. As a result, I vote no on almost all propositions on principle. Even if I agree with a proposition, there are few issues that I think it should be elevated to level of the state constitution and should be untouchable for decades. And to emphasize how the system isn't that useful, I'm not sure if there have been many, if any, landmark ballot measures (since like 1920) that the legislature or judiciary wouldn't have implemented anyway. After all, it took the California courts to legalize gay marriage and the US Supreme court to re-legalize it. I'm not saying we should do away with the system altogether, but it needs to be reigned in with stricter signature requirements and other measures to ensure that the issues we're voting on are actually important and, if they're not important, aren't quasi-permanent.
So tl;dr, basically the California system is flawed because there are too many silly and weird issues and the system amends the state constitution causing us to get stuck with regrettable propositions for decades. In connection with the overall thread, I don't think it should be the role of the average voter to decide on complicated and obscure issues but the buck is often passed to voters in CA.
