I count it as failed if the government is spending money from the budget on unnecessary items while any social problem is still unresolved. That includes homelessness, poverty, health-care for the poor/needy/elderly, etc. Same goes for crime, road-fatalities, and a multitude of other things we expect of the government. These should be largely solved problems by now, especially with the technology available these days.

Either way, yes you are most likely statistically right. Spending on healthcare, poverty, and disabled individuals probably directly correlates with their well-being. You were presenting a case against a hypothetical ideal, and claiming it would not be able to fix social problems in a non-idealized setting. The counter-claim to that is that those very same things are not resolved in a society almost-exclusively run by state-governments, either. Whether 1st world or otherwise.