Ignoring the people who are just here for another Libertarian pinata party, here's the deal. Libertarianism is attractive because:
- It presumes that most people are Good
- It presumes that most people are Rational
- Meritocracies can work
Therefore, you don't need or want a government restricting you from doing things a Good or Rational person wants to do.
There are a lot of people who falsely accuse libertarians of hating poor people or saying "fuck you I got mine" and so on. In reality, libertarians believe that since people are Good and Rational that a market of these people will eventually lift everyone up. The Racist Businessman, therefore, would go out of business because the Good and Rational people would not patronize his stores, nor work for him; causing him to miss out on both customers and workers.
Libertarianism therefore distrusts power that is centralized under a force outside the market. If somebody claims power via the market, it follows that they have provided goods and services to the market in order to claim that power. So their power is justified and is enhanced by doing Good Things. They must also do things efficiently because if they do not, the competition will beat them and claim the power/wealth.
In contrast, a Government wields massive power and has no competition. This generates a situation where the market can reach outside the market to a non-market power and use it to stifle their own competition -- which is something we see happening constantly today and is how we've shifted to corporatism. Keep in mind that libertarians do not favor corporatism, though some would tell you otherwise.
The OP asked: "While this sounds very refreshing, one has to wonder how a libertarian would respond to the reality of third party forces that can pressure the people in a far greater way than the government can. For example, telecom companies or healthcare companies."
The way they would respond is to point out that those companies have gotten as powerful as they are because of the government, not in spite of it. Our government puts in place many policies that are meant to aid certain companies over others, create monopolies, etc.
The main flaw with libertarianism is that it's too idealistic. But then again, that flaw is what draws so many to it.
To many a libertarian, the goals of a modern government should be:
- national defense
- control/ownership of
Natural Monopolies -- public utilities and such
- dissolution/obstruction of anti-competitive-market practices (other monopolies, etc.)
- potentially fire/police in certain areas
... and that's mostly it (though I'm sure I'm forgetting a few things).
The government will be less efficient at most things when compared to the market (except in cases of natural monopolies, see above)
Things the government should not be doing:
- creating/enforcing drug laws, prohibition, etc.
- banning sale of soda containers that are too large
- searching people at airports
- starting wars/policing the world
- interfering with people doing things that don't harm others, etc.