In my opinion, I partly agree with the idea that all levels of education should be free to public. It's of great benefit to improve the overall quality of a nation's population. However, there might occur some issues if higher education being completely free of charge.
As we know, no input no output, the quality of education somehow depends to a certain extent of economic condition, let alone higher education institutions.If higher education institutions no longer have money incomes, how could they support the salary of staffs? No matter the quality of teaching and studying.
However, if the government like to pay for their people's education, that's another story.