One "why" is obvious: Separation of powers. The uniquely drastic separation between executive and legislature in the US is a problem particularly for many "liberal" policies, including health insurance. In other jurisdictions such policies usually involve a great deal of delegated legislation, something that is difficult in the US. As a result, any reform effort invariably gets bogged down in the details of 2000 page monstrosities. (Which, incidentally, is also due to another important institutional factor: single seat constituencies, meaning independent mandates and greater incentives for rent seeking on the part of the individual legislator.)
Another "why" is one of history. While it is hardly my area of expertise, I know enough to know that the position of unions is drastically different in the US, and in many ways much more precarious. As a result, they have an outsider's position similar to their French brethren. (I read a beautiful analysis recently about the French propensity to strike, as explained from the traditional French distance between the unions and the halls of power, as compared with the Dutch and German systems, where there is more consultation between the government and the unions. Unfortunately, however, I can't find it anymore, so I can't link to it.) This, in turn, causes them to rely more on the methods of conflict - and to resist attempts to curtail their ability to rely on such methods - than on the methods of consensus. What many European social-democrats have in common with their christian-democratic cousins is their reliance on consensus and consultation. In the jargon of the Dutch christian-democrats, unions are part of the "maatschappelijk middenveld", the middle ground between government and society. In such a corporatist/syndicalist society, there is no reason for unions to go on strike (which Dutch and German unions rarely do), and there is no reason for the government to unilaterally regulate every aspect of everyone's behaviour. Instead, they make a million different "covenants", whereby everybody promises to act in good faith based on certain general principles.
To be continued when I have more thoughts...
UPDATE: This BBC article discusses some of the history points I mentioned.
P.S. Another interesting topic to look into: European courts often treat human rights issues from a proportionality perspective: Is the infringement of right X proportionate to goal Y? An case in point is the burqa ban decision of the French Constitutional Council. In the US, this issue is resolved with levels of scrutiny: rational basis review for the little sins, intermediate scrutiny for the whatever-inbetween category, and strict scrutiny for things like core free speech and discrimination based on a suspect classification. So I've been wondering: substantively, is there a lot of difference between these approaches? Do they actually lead to different outcomes? Or is it a different way to phrase the same question?