You argument is not in favor of the poor. Given the way taxation works, free healthcare and education provide opportunities for lower incomes that aren't available for private services. When education is free (popular phrasing for government paid), a poor person with no income can get a free education and usually financial support and actually get a degree. If healthcare is free, the burden of the individual is carried by the society. As for 'standard libertarian arguments', you might as well say 'myopic perspective'.
