It’s interesting you should argue that there are bigger libraries showing the opposite, when virtually all your links come from the same site. Funnily enough, the site itself seems to mostly make statements without any references to published literature to support them.
Lasik is an interesting example of a technology that has progressed rapidly in a short space of time, reducing costs very significantly as it went from a high-risk and problematic surgery to a short and extremely low-risk procedure. How this demonstrates the efficacy of a “free” market is anyone’s guess, especially as a big part of the price reduction was the FDA’s large-scale study that showed how effective Lasik is.
As to your last point — as far as I can tell, this is simply an assertion without any basis in fact. The article linked makes the hilarious assertion that socialized medicine is evil because it gets rid of the private system, but does not in any way speak to a “clear and demonstrable” correlation between rising healthcare costs and socialized medicine. On the other hand, as I demonstrated in my piece, there are innumerable examples whereby socialized medicine has substantially lowered the costs of the healthcare system.