Upon viewing the 5 videos, I actually found them incredibly informative, yet concise and easy to digest.  In answering the question more broadly, I would have to say that our 15% uninsured is, in large part, due to our fierce belief in the unassailable superiority of the "free market".  Interestingly, it was shown that even in other Capitalist nations, it was admitted that what is best for the economy may not be best for health care.  The president of Switzerland himself, a conservative party member, voiced that 100% free-market health care causes you to "lose solidarity and equal access".  Further, I feel that we also seem to have a history of being a very polarized or "all or nothing" society.  This may lead many to the mistaken assumption that we either have a choice between entirely pure, free-market health care or a single government-run system, with no grey area in-between.  I thought these videos did a fantastic job of showing that is entirely false.  Just as we saw with Taiwan, you can have an immensely successful health care infrastructure based on an amalgam of alternative systems. 

Another main reason for our fierce adherence to the current system would be the profound fear in this country of all things "Red", in other words, any ideas or systems that could be interpreted as "communist" or "socialist".  While I am not aware of the depth of anti-socialism in any of these other countries, I believe just the fact that these systems are often referred to as "socialized medicine" is enough to defeat any hope of instituting a universal healthcare system in the US in the near future.  However, I found Switzerland to be one of the more intriguing examples, as they appear to have been as bitterly divided over healthcare as we are currently in the U.S.  The fact that the law was passed, even if only by the thinnest majority, in another country priding itself on staunch individualism, gives hope for a similar outcome here.

The true reason behind such a high lack of insurance in America is undoubtedly far more complex, but these were the main two reasons that leapt out at me through the PBS documentary.