Price fixing is a criminal federal offense of the Sherman Act. Not only does it affect competing businesses, but it also limits the price of items much further down the line that have nothing to do with the original vaccine. A fixed cost on one item like a vaccine doesn't account for the needles, sanitary faculties, physicians, components of the vaccine, etc., all of which vary in cost.
Price fixing a vaccine, versus subsidizing it, would affect thousands of private businesses and spur a flurry of changes across the health care industry, first and foremost would strike anxiety into the market, driving up prices. Resources become inefficiently allocated for the vaccine because of legal requirements, instead of pressing patient needs.
I see many people who want healthcare fixed via government monopolization, but it is my best belief that healthcare stays private, with various government subsidies, especially post-investigation of the VA scandal by the Obama administration.
Private (non-profit) healthcare has more incentive to fight fraud, specialize in pathologies, appropriately allocate resources, and most importantly, provide excellent, aboveboard care.