Private litigation ALSO has a nation-wide bureaucracy with an immense army of "conflict resolvers", and is often so inefficient that the litigation itself if often used by powerful corporations as a means of harassing their enemies. We need massive legal simplification, I agree, but that doesn't necessarily mean just moving to private litigation and being done with it.
Some private litigation firms will probably always be bloated and inefficient, but that's just great news to their competitors. It's no different than private retail stores: some are inefficient, but the more efficient ones tend to do better (or pressure the inefficient ones to improve).
The beauty of libertarian ideas are that you don't have to have ever been involved in anything to understand them. In fact, it helps if you haven't. http://raikoth.net/libertarian.html
Or more likely just result in the inefficient one (almost always an indicator of having more resources) buying the efficient one or simply undercutting them out of business, in order to maintain their status. It is cheaper to just get rid of the competition than to actually improve your own practices.
And how, pray tell, is a government solution (which is not only monopolistic, but uses violence rather than shady business tactics to maintain its monopoly) any better?
How is me depriving you of your ability to live (you know, get food, etc) via economic harm any different in violence than a government depriving you of your ability to live (via guns)? Is it because slow painful deaths by starvation, caused by a guy with a grudge are what you want for the world? Is it because that threat isn't really different other than the totemic difference of the removal of the word govermment (aka your magic symbol for evil)?
You need to define "depriving you of your ability to live." If you mean stealing someone's food or annexing their farm land, then I'm absolutely against that. If you mean choosing to not give someone some of your food, or causing someone's business to fail because your competing business is more successful, or choosing to not employ the, because they are unqualified or underperforming, then I find no blame. I do not believe that I have a moral, legal, or societal obligation to provide for anyone or everyone, but more importantly, I do not believe that a society where people are forced to do so under threat of violence (i.e. every government in history) will have less poverty.