The libertarian ideal assumes that the nautral state of business is competition, when in reality the natural state of business is collusion and consolidation. In a libertarian paradise, one of two things happens:
1. The major insurance companies collude, offering customers no choice in plans. All plans offered have loopholes where the company can easily dump the sick. Customers are given no choice, and insurance companies more or less write a death clause* into their policy,
2. The major insurance companies consolidate to the point where you only have one or two options, neither offering any real choice or competitive reason to chose one over the other. You accept whatever plan is offered.
In either case, start-ups are quickly squelched.
You more or less see this in the drug trade. In mexico, the drug market is more or less deregulated, since the government has no power to control the cartels. While the major cartels do squabble, they prefer not to compete against each other directly, as doing so tends to weaken both, allowing a 3rd cartel to grab for power. Regardless, upstart operations are quickly squashed.
You may argue that this situation is the result of government regulation. I'd agree, but point out that the only thing government regulation has done is artificially raised the value of the commodity. A commodity that is 'necessary' and sufficiently rare or expensive will tend towards the same result if left unregulated (see various oil and communication companies. See also diamonds, where the DeBeers conglomerate created the same artificial scarcity as seen in the drug trade.)
* Prior to the ACA, insurance companies did not have 'death panels' but they did have a 'death clause' in the form of a $3.5 million dollar lifetime cap on coverage. If you hit this cap, your 'pre-existing' condition would disqualify you from purchasing insurance from a competitive provider, and unless you were extremely rich, you clearly would not be able to insure yourself. At this point, you would be stabilized and sent home by the hospital as soon as your medical costs had left your family destitute.