No. People should be educated by the taxpayer to the point that they are productive, which is generally high school level.
If college were free, it would become a refuge from work, with many people going to school to party, paid for by those who work. Actually, many people ran up a trillion dollars of student loan debt using college to hide from the work place or earn useless degrees while partying. If people had to pay for college, either up front or over a lifetime, they would not take useless classes, use college to explore the world (at considerable taxpayer expense) or waste time.