This was the topic question in Zocalo's event yesterday.
If by higher education, you mean "4-year college" then pretty much, yes. It's been like that for centuries.
If by higher education, you mean "associates or trade tech" then, not necessarily.
It's relatively cheap here in California.
In a world in which the popular discourse from newspapers to educational institutions are championing and maintaining that they provide equal opportunity, we want the answer to the question to be no. We want higher education in its different properties to be for non-rich people too!
A few months ago the National Center for Public Policy and Higher Education found that high-income students on average find more financial aid their expenses than low-income students. What does that say about low-income students?
I think it says that they often don't know where to find the resources. I personally was intimidated whenever I had to take care of administrative work. I'll bet that they don't have too many friends or relatives who have done the college thing themselves. They don't have networks of people who've worked it and done the same.