Man, no. The solution to nationalized healthcare is the same as to the problems with education, infrastructure, etc. Broad policy changes at the national level, with implementation controlled by local entities that understand the specific problems of the community. Soviet-style monolithic government failed, we need a national program that implements large-scale changes while giving actual power to the people who live in the communities-- municipal and state level authorities, elected by the people they will directly serve.
The psychology i've had, and the anthropology I've had, and the nearly-20 years of experience I've had with human beings, tell me that people do not make the most "rational" decisions, especially when it comes to things like health which are complex and don't seem like immediate threats. People constantly make horrible decisions about their health, and that's their right. Smoke, do drugs, eat fatty foods, whatever. But kids shouldn't suffer for the sins of their parents. The fact that your dad spends his money on lottery tickets, or your parents are saving up for a house, or whatever the fuck, whether good use of funds or not, should not keep you from getting basic healthcare.
We have public education in this country because we believe every child deserves the same chance to be successful. Has this been entirely successful? No. Some people are born with inherited natural advantages (intelligence, discipline), and some are born with inherited advantages of a different type (my dad is a legacy at Harvard, my mom is in the yacht club with the head of the UPenn medical school, my great-grandpa invented ketchup). Does this mean public education shouldn't exist? I hope none of you will argue this is the case. Not to mention the fact that democracy cannot come even close to functioning without a well-educated populace. How is education a universal right, but not basic healthcare? Ridiculous.