That will happen either way. If you remove government controls, it only means the wealthy don't need to worry about usurping the government anymore. Wealth will still snowball, and other methods of crushing competition become available when the government method is removed. This is why I'm an anarchist. We can pendulum back and forth for eternity, and we'll never get a desirable result.
Given a choice between two directions in the meantime, I'd rather stay on the side that is at least ostensibly supposed to be about serving the people, instead of 100% ruthless winner-take-all-and-losers-can-go-die competition. That way when it is proven that the system has been sabotaged, there is the slimmest potential for people to organize on the basis of a common idea. At least when things suck, everyone knows it's because something is broken. On the other side everything can simultaneously suck but also be working exactly how it's supposed to even in theory, which thins the sociological glue of common understanding necessary for change.
Yet without the many government imposed barriers to entry, entrenched wealth would only last so long as it's possessor was capable with it (Shirtsleeves to shirtsleeves in three generations and so on). It's pretty damn easy to hold onto your wealth when your stock investments are basically guaranteed to go up by the Central Bank, your companies shielded from competition by high entry costs, and your bank grows by default because it's the first to receive cash from the Central Bank (meaning it gets the benefit of however many billion dollars, and the inflation doesn't kick in until some other chump receives it). Plus, if despite all this things go sour, you have nothing to fear because the government will pay you back for your losses should you be in danger of, god forbid, failing! Hell, if you're a bank in a "progressive" country, the government will promptly drop everything else and fleece it's unfortunate population for tax revenue on your behalf! Furthermore, when the economy is on the brink and things are looking bad, the fellows within the government will prioritize what will get them reelected above what might help; hence, you end up with passionate arguments about cutting a few million or hundred million from a budget of trillions, or else argue about things like the income tax on the richest 1% (which won't affect the absolute richest and most powerful anyway because THEY make money through investments and effective tax shelters like Berkshire Hathaway).
Yeah... just like you said, the system has been sabotaged. All you've done here is point out specific indicators that the government has been usurped, and turned against its intended purpose. And those who have the resources to spare will always dedicate some to the making sure things are that way. It's a dumb set-up that is doomed to fail repeatedly, but at least it provides people some channel for collective struggle. That's really the only difference. On the one hand, you have some means for people to pool their resources and have a chance of sticking up for themselves. On the other hand, you have get rich or be subjugated by the rich and that's it.
As for your claim about the longevity of entrenched wealth, I don't see it. Those who own the world's resources impose conditions for the rest of the world to partake of those resources, and they structure those conditions to be in their favor. That's how wealth entrenches itself. Whether they do that through influencing the government or through ruthless business tactics doesn't really matter. Actually, it does matter, because the average person has some theoretical voice in one, but not the other. Competition can challenge entrenched wealth, but so can a determined political movement.
If market competition were really so good at weeding out corruption while rewarding hard work and innovation, then Nikola Tesla wouldn't have perished destitute and forgotten, and elementary schools wouldn't teach children that Thomas Edison was the greatest inventor in American history.
Yet Edison made a disproportionate amount of his money through patents and IP, two things that are effectively artificial barriers instituted by the government. The end of the Gilded Age was a period in which every businessman tried to pillage every other by supporting government initiatives in their favour (be in strict regulations in quality/price/etc from large corporations or anti-trust from small companies) until power was far more concentrated in the hands of the government itself, government backed monopolies, and large corporations in heavily regulated industries.
Going by a free market, individuals accumulate wealth through producing things for their fellow man and trading them voluntarily for the benefit of both. I hire Jim to make shoes for me, I buy the machinery, etc for Jim to make shoes, I sell Frank the shoes in exchange for something I want, and then I compensate Jim for his energy and time in a second, mutually beneficial exchange. If, at any point during this (very simple) series of exchanges someone is dissatisfied, they can reject it and go do something else instead. Everyone is better off, as they acquired something they wanted for something they had but didn't want as much (be it time/energy, shoes, or money). Over a long period of time, I might even accumulate a pile of wealth, perhaps even enough to help my children go through life without needing to work. And that's just fine. However, any term longer than a generation or so, that wealth will dissipate unless those who receive it are careful with it. Notice how people who win hundreds of millions in the lottery don't become influential, powerful oligarchs despite having so much. And that's just fine too.
But see, the government doesn't need the voluntary consent of every individual involved. If I can make the government happy, I really don't need to serve anyone else well because I can use my connections to get the competition strangled by regulations and barriers that mean I can sit on my ass producing an expensive product without having to actually keep consumers happy. Now my wealth is firmly entrenched, as I can squash anyone who comes close to causing me to lose any of it.
Now, with Syndicalist Anarchism (which is what you advocate, I believe), you run into a variety of unintended problems. Okay, so you've succeeded, the government is gone, the workers own the means of production, and there are no rich people. First of all, you have the awkward problem that creation of capital goods requires capital accumulation, which basically requires wealth accumulation. But there is no property, only "possessions", so no one person is actually capable of bringing these into existence! That's why Syndicalism starts with "The workers seize the means of production" in the first place. There's no organization like a government that will create them either like in a regular Communist nation, and the largest organization at all, depending on which Anarchist you ask, is either a commune or the factory itself. So creating something
new requires that you manage to somehow convince one of these organizations to take a big risk for effectively no payoff. It also requires enforcers to crack down on people who would inevitably start bringing back capital accumulation, like people voluntarily working for others in exchange for passing off the risk ("I'll run this factory for you guys and take on all risks if it fails, so you get a guaranteed steady wage while my own will be determined by the success of the factory"). The practicality in the long run is lacking, if the experiences in Catalonia are anything to go by.
You say that liberals have no solutions and conservatives do.
Individual liberty is served by social and economic justice. Libertarians claim to promote liberty, but when their policies inevitably lead to a system that disenfranchises the majority of people and makes the ability to express rights so grievously unequal, then they are not truly promoting liberty.
Sorry, but right now the conservative solution is destroy America and return to more conservative times when the plutocrats had absolute liberty to rape, pillage, maim and kill in the name of their god, money or just for kicks and everyone owed fealty to them for the privileged of bondage.
Well, no. Liberals (in the American sense of the term) create the illusion of safety and security for the poor while simultaneously happily backing the interests of the wealthy and influential indirectly. In Europe even moreso, a state of dependency is created in which many people effectively require the welfare state to continue to live their lifestyles, which in turn motivates them to support it, which leads to more people becoming dependent on the government, and so on and so forth. Over time, this comes to include important sectors of the economy. Yet when push comes to shove, they quite happily throw those dependent on the government to the wayside and bleed them for cash to pay back their friends in the banking industry at the expense of nearly everything else. Hell, in Greece, a country that used to have one of the highest ranked healthcare systems in the world, basic drugs like Aspirin are hard to find. The people think the government really cares about them under this system, yet the government is as much in the pocket of the powerful as ever, it just creates the pretense of equality and caring.
Conservatives (again, in the American sense) have the problem of being notoriously mushy on what they want. "Let's cut taxes!" they say first, without even opposing the spending that requires those taxes in the first place. Then, they get a bit more principled and say "Let's cut spending!". But what spending? Certainly not Social Security, Medicare, Medicaid, or the Military, which combined are something like 80% of US government spending! So instead they cut from insignificant programs and make a big deal about it, while the liberals similarly make a big deal out of it lest people figure out the game they're playing. The most honest of conservatives at least understand the problem and part of the solution, but they point at a mythical picture of the past as the "ideal", as though there was ever a period in American history that was great. Radical change on present systems is required to achieve the ideal that the most honest of conservatives and libertarians want, not simply "rolling back" to the 1950s, 1900s, 1770s, or what have you.