There are many collective action problems (i.e. tragedy of the commons)that crop up in capitalism and other systems that only a government of some sort is well suited to address. A pure laissez faire government would be unable to address these problems, to the detriment of all. Mixed systems work best, which is certainly borne out by the data - and yes, the United States is a mixed system too, and it works pretty well.
What's interesting to note in this concept is that one of the means that has been theorized to solve the problem is private ownership. I will posit some anecdotal evidence.
We are issued by my department AR-15 rifles. They continually get beat up, suffer from mechanical problems, have bent sights, etc. The same thing for our shotguns. We recently were allowed to purchase our own rifles. Although they get used and by necessity suffer cosmetic damage due to training, they are well-maintained and cared for by the individual officer owner.
But, as Elder pointed out, it is not the system but people, which are the problem. Pure Communism may work out great in it's niche, and the same can be held for pure Capitalism. The problem is when you interject people into the mix.
The problem with the tragedy of the commons as I see it is that it has the underlying assumption of the grazing metaphor is that it is rational for the herder to over-exploit the resource for short term gain. This is an assumption that I don't necessarily hold to be true. For instance, how rational is it for me to put short term gain over long term insolvency. Not very.
Of course, the way that we regulate businesses in the U.S. may actually be causing more problems then it is solving. There is not a day that goes by here that someone complains that corporations are doing x, y, or z and destroying the middle class, engaging in class warfare, etc. But they are doing so because the government is allowing it to occur. Not only that, but the government is enforcing those regulations which are allowing them to do so. Not only that, but they are beholden to those corporations due to monetary influence, whether by straight bribery, promises of lucrative jobs after they leave office, or money towards their re-election campaign.
Perhaps if we make people personally liable for the decisions that they make which harm people, rather then the corporations, then we could significantly reduce, if not eliminate, the problem.
But, if we had limited government that would allow the people to decide whether the corporations business practices are such that they would support, then what is the problem. I am not against all government intervention. After all, when a resource is owned by no one, there must be some means of fairly distributing the benefits. This will by necessity leave some people out. But this is completely different then the idea of communism in which the state owns all property, and the individual owns nothing.