Nationalized healthcare might help with certain things but it can't create capacity out of thin air. Just because the government theoretically covers everyone doesn't mean that services are actually available when needed. In general the countries with the highest levels of nationalization also have the most problems with shortages. When everything comes straight out of the government budget there's always a political tendency to cut costs by reducing provider payrolls, imposing waiting lists for expensive treatments, or refusing to cover certain treatments at all.