There is no such thing as 'free education fully financed by the government'. A zero-tuition college education simply means that instead of the students bearing the cost of attaining their degrees the taxpayers bear it. Students and parents misperceive the price of education, considering it to be free, even though it comes out of their pockets in taxes.
And why should low-income taxpayers finance the education of wealthier students? Proponents of state-financed education argue that absence of government help would put higher education out of reach of poor students. But I tend to disagree in that there are no 'poor college students'. College-caliber students possess great wealth in the form of human capital. Anyone headed for college has enormous wealth in the form of intellectual capital and will receive earnings from his/her college education. So, the benefits of a college education are essentially reaped by the individual acquiring higher education.
The future earnings of the individual typically constitute an adequate return on the gross investment in abtaining higher education. Moreover, providing free college education to all is a rather inefficient way to serve the interests of poor students since a large proportion of students who acquire higher education come from relatively well off families.
There are many negative aspects of government-financed higher education.
Free education leads to overproduction and waste. But, isn't it good to have more young people with degrees? Don't we need a more educated workforce for the more demanding jobs that will dominate our economy in the future? The answer to these questions is 'no'. By putting more people in colleges we end up with unmotivated students who lower the standards demanded by higher education. In his book Generation X Goes to College, Peter Sacks explains how he was driven to make his courses intellectually vapid,