Yes and this generates other tensions: those who fail the almost free higher education are totally left behind, with almost nochance to catch up (statistically speaking).
That doesn't seem true in Denmark, at least. First, even minimum-wage jobs with no education requirements will pay a living wage (minimum wage is about $37,500/yr, plus benefits and 5 weeks vacation). So, economically speaking, people with no education are not that far behind, nothing like American minimum-wage workers. And second, going back to university as an adult is pretty common.