The libertarian argument for having universal coverage, is to have a private option and an option to opt out of government provided healthcare. As in... Medicare...
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The flaw in the OP libertarian argument, is abolishing insurance. Universal coverage and private insurance coverage, are not mutually exclusive.
In general, the problem with healthcare on pure libertarian vision, is that your principles mean shit when you break your leg and chose to not have insurance. The following choices will likely cost more to the populace, than it would have been to be insured. In the end, it’s embracing irresponsibility and having no understanding of human nature.