Capitalism only works when society keeps it in check through government
Not necessarily (depending on if you mean society keeping it in check in all situations, or some) - there are some situations where it is far better for government not to intervene in the markets, since they can end up making things much less efficient and make everyone worse off as a result. There are other cases where the market failure is so great that government intervention, although not perfect, would be a better proposition.
Meanwhile, since capitalism is effectively the private ownership of assets (and the operating of these for profit), saying it is a failure implies that the next best alternative is better. The next best alternative, that is the public ownership of assets with an absence of profit, is communism, and compared to capitalism is an absolute disaster economically speaking. So no, capitalism when evaluated against the alternatives is certainly not a failure but rather a stunning success.
The truth of this statement is illustrated by the pandemonium we see unfolding in the market today. This chaos is thanks to decades of deregulation which has allowed a small number of rich folks to get richer while the majority of society has suffered
Well my understanding of the root causes of the various problems in the markets (I'm assuming this is referring to financial and/or property markets? I'm not 100% up to date on US current affairs though so feel free to clarify if I've misinterpreted) is far more to do with a failure of contracts and lack of foresight into peoples incentives than capitalism. That is, companies didn't seem to think through that if they rewarded people when things were good, and could only punish them with unemployment when things went bad, then they were encouraging excessive risk taking. The problem with this? You end up with employees of a company (who effectively make up that company) then turning into risk lovers and taking on 'projects' that would be expected on average to yield their company a loss rather than a gain. A quick example: Say you have a possible project that you can choose to undertake on behalf of your company; If things go well it yields $200,000. If things go badly, the company loses $2,000,000 and you lose your job. The problem is that while the company will suffer a massive loss if this project fails, your loss is restricted to whatever your salary is, such that you don't choose the profit maximising choice.
However as with anything, the solution is rarely simple. Firstly, the problem could just be due to a lack of information/awareness of the problem. If the company realised it was encouraging such behaviour then it would be in it's interests to change the contracts at once. Hopefully given what has happened many companies will have learnt their lesson regarding this. The case for government intervention in this situation would therefore be to look at what caused the failure of investors to realise this problem and change it, or alternatively the people they appointed to manage the company to realise it+rectify it. Such intervention to rectify market failure (imperfect information) could therefore be justified. However the most efficient method is still to rely on private ownership and the maximisation of profit as a driving force. This is because it is the most efficient one, that maximises the wealth of the country.
It has allowed corporations and businesses to operate without impartial oversight thanks to the 'honor system' belief that they would police themselves and act in the best interest of the greater good. What has happened is instead the exact opposite
Capitalism isn't about companies abiding by an "honor system", it's about them maximising profits. Thus if behaving ethically would enhance their reputation and generate increased sales as a result, the cost of such behaviour could then be justified. However if the costs would outweigh the benefits, then don't expect companies to undertake such action. That's the advantage of a capitalist system - you can trust companies to (generally) take the action that maximises their profits. So long as there aren't harmful negative side effects to this to society that aren't incurred by the company, then this is fine. Where you have such externalities, then you have a case for government intervention if the externalities are of sufficient size. For example if a company is producing an item that lets off harmful gases, they will suffer a small cost, but society a much larger one. The ideal solution is for society to then impose a tax on that product equal to the environmental damage produced, so when the company then chooses the profit maximising output for them it is also the output that maximises the benefit to society. This is of course making various simplistic assumptions (e.g. that society knows the exact amount of damage caused so the tax imposed is the right one), but is to help illustrate the point that you can use the capitalist framework to maximise society's benefit.
As for your letter, it is only focusing on the dangers of markets open to speculation. The downside is that such markets are likely more volatile. The advantage is that they are generally much more efficient, with prices able to reflect the actual value of a good much faster. That is, if an item is overpriced by the markets, if you have speculators then they can step in and short that item, knowing it's overvalued. When the price falls back to it's real level they've made money, and it works same way for price falls; buy it when you believe the price is below what it should be, and when it returns to it's true level you've made money. It's not all perfect, and the advantages are much more general and dispersed to be noticeable compared to the obviously more noticable problems say of a speculative bubble.
Not to say there should be no regulation of such markets though - for example insider trading should be stamped out wherever possible since that can have massive repercussions on the market efficiency. That is it results in much higher buy-sell spreads on the part of traders, who in turn have to insulate themselves from people with inside knowledge trading on it, and in extreme cases can lead to a complete failure of the market (e.g. if insider trading is rampant, and someone wants to buy an item you're selling for $10 a unit, then you're going to think they know something you don't, and that $10 is too low, so you won't sell. If they want to sell you them at $10, again you'll think that $10 is too high, and so won't sell).
The way to do that is to re-enact many of the government regulations that were stripped in the last few decades in the name of free-markets and globalization. And enforce those regulations!
Not all regulations are good though. In many cases they needlessly complicate things, lower efficiency, and end up hurting the same society that introduced them. In some cases they are needed, but a 'the government knows best' approach is just as dangerous as one advocating the abolishment of all regulations.
