Human capital does have externalities - i am better off with an educated spouse , educated neighbors and colleagues. There is more knowledge and progress for everyone. But you are right that the educated person will, on average, internalize most of the benefits through higher wages and happiness.
What you argue is also true for health care, isn't it? It is mostly a private good. But governments spend a lot on it and the WHO has announced a goal of providing it free of charge by 2030 to all poor who cannot pay. While more and more public funds are diverted to health care for the already ill, services to prevent spread of diseases are more and more underfinanced.
Very small public goods investments in prevention and prepared disease control authorities could have nipped in the bud the now raging ebola outbreak in West Africa . But the investments were not done. They will never be done if history is our guide. Look at cholera in Haiti. Donors will just build more hospitals and clinics there, staffed with mostly absent government health care workers.
So I believe that The World Bank should impose conditionality on countries that do not provide basic public goods to prevent rising disease burdens in the future. The first use of public money should be public goods, goods which can be provided only by government and that give the largest benefit to the country.
According to the World Bank, it is not access to health care, but rather educating girls that is the most efficient and effective way to improve population health status (health of the girls and their families and communities). Girls' education is then in large part a public good because the girls and their families do not get ill and so do not need the health care services that all governments consider increasingly to be their responsibility.