People aren't going to have equal outcomes. They also aren't going to have equal opportunities. Trying to change this a fool's errand.
Society can make spending choices that encourage equal opportunities.
Low/no tuition fees for post-secondary education mean more students can continue their educations.
Universal health care means people are not tied to their jobs because they fear losing work-related health insurance.
Good parental leaves mean women and men have more options for work/family life.
And so on. These are all social choices.
None of those create equal opportunity. Just to go with the third, since it's extremely obvious, some families have 2 parents, and some families do not. You cannot adjust for that, unless you decided to off my Dad somehow. Perhaps through a war or a bubonic plague, which is what the original article suggests is the ONLY way to create equality.
I don't care if the average person goes to college, they still aren't going to have the opportunities of wealthy kids unless you prevent their parents from helping them in other ways (connections, job advice, additional rent money, whatever).
EDIT: If you want to spend money on it, fine, but I'm not interested wasting money on an equality dream. Expanding coverage to the remaining 20 million uninsured is probably going to cost another $200 billion per year. Trying to correct for the fact that everyone has crappy plans with high deductibles is going to cost several hundred billion more. Bernie Sanders free college is $75 billion. If you want to increase all the education spending in the US to $18,000 per pupil, that's another $300+ billion.
Now you're talking another $1.2 trillion in spending, which is a 36% increase in taxes, and we're still not going to be equal, so someone is going to come back in 10 years and want even more. I haven't even touched retirement, or pre-K programs, for instance.