What an incredibly horrendous idea. Increases in student debt are the result of students making bad decisions about the schools they attend. Students are enabled by the federal government that created and supports student loan programs that allow these young kids to qualify for insane loan amounts.
A better solution would be to restructure the current student loan programs such that student debt load is capped at some reasonable level. The effect would be that students would be forced to make more rational choices about the schools they decide to attend and how they pay for their education. The education market would respond accordingly as more money flows into community colleges, state schools, and other lower cost education options. Costs would go down.
"Free" college education supported by general taxation or more targeted taxation would have the undesirable effect of disconnecting personal spending choices from personal spending consequences. The result: market distortion that pushes costs up at increasingly unsustainable rates and second order pressure for education rationing by the federal government.