The old Robert Reich/Bill Clinton model of how to fight inequality -- through more education -- has failed utterly. Getting more education certainly helps some people escape from poverty but there is nothing automatic about this, and it depends on the availability of good jobs and the ability of people to find them and do them:
Handing out more high school and college diplomas doesn't magically create more good-paying jobs. When more credentials are chasing the same number of decent jobs, what you get is credential inflation: jobs that used to require a high school degree now require a college degree; jobs that used to require an Associate degee now require a Bachelor's degreee; and so on. . . .
Poverty is really about non-working people: children, elderly, disabled, students, carers, and the unemployed. The big things that cause poverty for adults over the age of 25 in a low-welfare capitalist society—old-age, disability, unemployment, having children—do not go away just because you have a better degree. These poverty-inducing circumstances are social constants that could strike anyone of us and do strike many of us at some point in our lives. To the extent that education does nothing to provide better income support for those who do find themselves in these vulnerable situations, its effect on overall poverty levels will always be weak, or, as with the US in the last 23 years, totally nonexistent.