Yes, China's stock market woes are an embarrassment. But not in the way free marketers think.

Now that the precipitous slide of China's stock market seems to have abated, we can step back for a moment and ask what, if anything, is to be learned.

One takeaway that's coalescing in the media is that China's ruling elite embarrassed itself. The government is on record pledging to allow markets to play a "decisive" role in directing resources, and the smorgasbord of emergency measures the government pulled out to stop the slide made "a mockery" of that promise, Scott Kennedy of the Center for Strategic and International Studies told The Washington Post. "They were spending their hard-won credibility in an effort doomed to fail," added Daniel Rosen, a partner at the advisory firm Rhodium Group.

The Week's own Pascal-Emmanuel Gobry argued that the events demonstrated the superiority of Western rule of law, despite the seeming ease and convenience of authoritarianism.

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None of these points are wrong, per se. China has certainly embarrassed itself. But these critiques do miss how China has embarrassed itself, and in a way that's important for debates over economic policy.

Let's work backwards, starting from Gobry's point. It's absolutely correct that the rule of law is a critical "social infrastructure" underlying the prosperity of America and the West. But it's not actually clear to what degree a lack of that invisible infrastructure is a problem for China.

The government there didn't unexpectedly rob a bunch of people and businesses and then funnel the money in another direction. Consider ObamaCare or the 2009 Recovery Act here in America: Whatever you might think of them on the merits, they were perfectly lawful, even while they decisively altered the economic landscape businesses are presented with, which is what China did. (Of course, the U.S. runs economic policy by democratic consensus, while China runs it by dictatorial fiat, but that's a separate can of worms.) Rather, a better description of China's problem is that it simply engaged in bad policy.

Over at Vox, Max Fisher has a good summation of the problem: China's export-based economic model requires that it remain poorer than its trading partners. Now that China's well into its wealth development, it needs to shift to an economic model in which a well-off middle-class consumer society within China provides the demand for its internal economic activity. That means less madcap industrial development and massive government boondogles, and more institutions that ensure economic prosperity is broadly shared, so everyone has purchasing power. Think something like the Nordic social welfare model, but China-sized.

The problem, as Fisher lays it out, is that a lot of mid-level government officials in China are deeply entangled with the state-run enterprises, and thus benefit from the boondogles and don't want the government to move away from them. If anything, China's political institutions are too decentralized, and this has allowed government officials to engage in cronyism on an epic scale. The stock bubble and burst appears at least partially connected to this tension — unable to break away from massive infrastructure and construction projects, but still wanting to encourage more use of private financial markets by Chinese citizens, the government just decided to do both. The result was a massive run-up in stock investments, largely detached from the underlying flow of supply and demand.

Now turn to Kennedy and Rosen's comments: Who exactly did China lose "credibility" with? Certainly its modest — but vocal and growing — urban middle class, who understand investment in China's relatively young financial markets as another step in their economic rise.

But this wasn't a commitment by the government to Chinese investors to "liberalize" its markets, per se. It was a commitment to maintain prosperity. If anyone cares about introducing more market forces into the mechanics of the Chinese economy, its Western elites. These are the same people who have belatedly realized that their championing of fiscal austerity and tight money, especially in Europe, has been dragging down economies since the 2008 collapse, and brought Greece especially to the edge of utter ruin.

As America and other Western countries have aptly demonstrated, you can follow "the rules" of free market capitalism and still grossly fail to achieve broadly shared participation in growth, or even basic economic justice. Worrying about the good opinion of the CNBC crowd is not what China needs to be doing.

Yes, the country's government should allow market forces to play a bigger role in determining where cities get built and what industries live or die. But what China really needs to do is ensure that, underneath those market forces, the massive wealth produced by the Chinese economy is spread as broadly as possible, from the bottom up.

That's what makes China's panicked efforts to shore up its stock market embarrassing. Not that it failed to live by the free market honor code, but that it wasted resources rescuing what amounted to a gambling casino for its upper class, rather than using those resources to continue lifting up its poorest members. Like most other countries' stock markets, the ups and downs of China's Shanghai and Shenzhen indexes have little to do with the ups and downs of the real economy. The government pumped money into them because their fall (which stopped well above where they were a few years ago) was a political embarrassment.

What this boils down to is the need for China to make better policy choices. As Fisher points out, what's stopping China from doing so is the design of its government. China's mess of overlapping cronyist industrial-political fiefdoms is not structurally the same as America's problem with the filibuster, the Senate, and the mass of veto points in our legislative system. But it's producing a very similar policy sclerosis. Arguably, that's the thing China most immediately needs to fix.