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".