Not always for college education. It was mainly after WW2 that the expansion of state universities and government programs like the GI Bill and others greatly increased access to college education by those from non-high income/wealth families. During that time period, some of the most prominent private universities like HYP also shifted toward having a higher percentage of their students being admitted for academic strength, rather than mostly as scions on inherited wealth (though remnants of the latter remain in legacy, celebrity, and development admissions). It was also somewhat later that mandated racial segregation in education in many places began to end.