A vast literature shows parental education significantly affects children's chance of attaining higher education even in high participation systems (HPS). Comparative studies further argue that the strength of this intergenerational transmission of education varies across countries. However, the mechanisms behind this cross-national heterogeneity remain elusive. Extending recent arguments on the "EE-SD model" and using the OECD data for over 32,000 individuals in 26 countries, this study examines how the degree of educational inequality varies depending on the levels of educational expansion and skills diffusion. Country-specific analyses initially confirm the substantial link between parental and children's educational attainment in all HPS. Nevertheless, multilevel regressions reveal that this unequal structure becomes weak in highly skilled societies net of quantity of higher education opportunities. Although further examination is necessary to establish causality, these results suggest that the accumulation of high skills in a society plays a role in mitigating intergenerational transmission of education. Potential mechanisms include (1) skills-based rewards allocation is fostered and (2) the comparative advantage of having educated parents in the human capital formation process diminishes due to the diffusion of high skills among the population across social strata. These findings also indicate that contradictory evidence on the persistence of educational inequality in relation to educational expansion may partially reflect the extent to which each study incorporates the skills dimension. Examining the roles of societal-level skills diffusion alongside higher education proliferation is essential to better understand social inequality and stratification mechanisms in HPS.