We know that there is an efficient model for delivering healthcare, which is a government provided/heavily-regulated healthcare market. We know this because dozens of industrialized nations successfully operate in this model, with dramatically lower costs than we have here in the US. An existence proof is usually the simplest kind of proof.
Some people talk about a hypothetical second workable model, which involves a massively de-regulated free market system. It's important to note that nobody has successfully deployed this model in an industrialized nation, and it's not clear if it can even be implemented in practice -- for political as well as practical reasons (unregulated medical providers tend to kill people, so voters enact regulations, and then you're on your way out of the sweet spot.)
Whatever your preferences, the important thing to keep in mind is that while both of these two points may exist, the points between them are highly suboptimal. Removing 10% or even 50% of the regulations on our current healthcare system is unlikely to produce a substantially more efficient system. It produces a new system with most of the weaknesses and entry-barriers of our current approach, but replete with massive new profit-taking opportunities and substantially worse protection for patients.
This is why two decades of political infighting in the US have failed to fix healthcare. There is literally zero chance that the working, de-regulated system is going to come into existence. There is some probability that we can get closer to regulated single-payer, since we already have Medicare and it's much more efficient than private insurance, even though politicians have restricted its bargaining power. There is an overwhelming probability that in the process of trying to deregulate the current system, you end up making everything substantially worse.