There is an old Milton Friedman video floating around which dates back to the 1970s. At the time he was spending a lot of time trying to convince people that oversized governments weren't a good thing.
One of the very salient points he makes to a detractor is that if you limit the size of the government, you - by nature - limit the power a corporation can obtain. If the government has limited powers, so it goes that a corporation can gain limited powers - it should be impossible for a corporation to gain more power than a government.
It's the essential point that everyone skips over - they see government powers failing to check corporate growth, and so want more government power. If you take this to the argument by absurdity, you end up with a fascist government that exerts total control over the people, and then licences that control out to selected corporations in return for cash and favors.
The problem is human nature - and the solution must be to design a system that makes the assumption that humans will try and gather power and abuse it. It's the same concept as term limits but applied across a much broader spectrum.
Consider this "very salient point": "if you limit the size of the government, you - by nature - limit the power a corporation can obtain. If the government has limited powers, so it goes that a corporation can gain limited powers - it should be impossible for a corporation to gain more power than a government".
This point is BS. There are places where corporations (or even one corporation) have more power than the government everywhere around the world, especially in Africa and Asia. There are entire countries where the government is just paid lackeys and a front for some mega-corporation. There is even a term for those, they are called "banana republics".
The limiting of the argument to "one corporation" is especially BS, since even if a single corporation cannot get "bigger than the government" in a place like the US, the "corporate interests" can and do get bigger than the government.
Despite fighting in the market (and that, only if they are serving the same market, which, say, Google, Exxon and GE do not), corporations also agree on a lot of things. For example media companies agree on SOPA and PIPA and a thousand other things (drm everywhere, destroy cinematographers unions, etc). And all corporate interest's also converge on a lot of things, like tax deductions, being able to fire any employee at will, lower minimum wages, unpaid overtime, etc.
Consider a country where there is no public health coverage. What will happen will not be "competing health services for the benefit of the customer" but an emergence of a health industry cartel and the total dependence of the people in it. Things that need big scale and resources, like building, buying equipment, and running a hospital or a bank or an insurance company, have been seen time and again to build cartels with "competitors" and kill competition to maximize profits.
(See also: http://www.technologyreview.com/blog/arxiv/27512/ , but one can also see it from experience, if one follows the political/social history of more than one country --something easy to do in Europe).
People talking about the limiting of the power of government always have in mind the equation "government = some politicians who abuse their power", and never "government = the only power body that is elected and somewhat controlled by the general public".