What's your evidence? What do you mean by "destabilization"? What do you mean by "concentration"?
While I think it's fairly well understood that economic winners tend to use the political process to entrench their position in anticompetitive ways, your exclusion of "cronyism or corruption in the public sector" seems to suggest some other kind of destabilization. Do you mean a Marxist revolution? If so, that's not a hypothesis supported by evidence, as there's never been a proletariat revolution against capital as Marx envisioned. Which of course doesn't mean the hypothesis is wrong, merely that it's unproven. The closest thing is probably the French revolution. That could be called a proletariat revolution, but it was certainly not a revolt against capital.
The term "concentrate" seems to imply a limited supply of wealth and income that is being reallocated to certain individuals or institutions. But capitalist wealth is primarily premised on economic growth, not on redistribution to those at the top. Material standards of living at every strata of society continue to improve.
To the extent that capitalism leaves classes of society behind, it is less about material inequality and more about dignity, autonomy, and finding meaning in one's life. But I think if we expect an economic system to provide meaning to our lives, we're asking too much, and the problem isn't solved by more income. Ask the average lawyer at a top law firm (where depression and alcoholism are rampant) if they fill fulfilled because they're among the highest paid professionals in the world.
Also, even though it's true that capitalism leads to wealth and income inequality, so far in human history, capitalism appears to lead to less inequality than any other system people have ever tried (barring stone-age tribal societies).
None of this is to suggest that we shouldn't redistribute income or have a welfare state. Just that it's questionable whether capitalism requires it.
Why is the failure of a business evidence that capitalism doesn't work? You do understand the entire premise of capitalism is that businesses are constantly failing, right? Bankruptcy is part of that process. The government propping up failing companies is actually interfering with capitalism.
Now, interference might be justified in some instances. For instance, I think it was absolutely the right call to bail out the banks, as failing to do so would've caused far worse economic harm. But I think that afterwards, we should've broken up the banks and imposed a size limit on financial institutions. There is strong evidence that banks can maximize economies of scale at far, far smaller sizes. There is also evidence that the reason banks have merged to such large sizes is specifically so that they can offload their risk to the public. Because their failure would endanger the financial system, they can pursue higher profits at higher risk, knowing that the public will always bail them out. A simple limit on the size of banks would've been a far more effective reform than Dodd-Frank, which in many ways exacerbated the problem. Compliance is so complicated that it requires very highly compensated lawyers, which provides an advantage to the entrenched market leaders. This is commonly misunderstood: Big business LOVES regulation because it protects them from nascent competitors.