In a nutshell
A college education has exactly the same purpose as that of the first twelve (or fourteen) years of public education: an educated populace benefits the United States of America.
The whole idea
It seems many citizens think that public education is for the benefit of children. WRONG! Public education is for the benefit of the public—the people of the nation at large—else there is absolutley no reason to pay for it out of tax dollars. And to cite the obvious, the reason public education benefits the nation is because educated citizens make better decisions in elections, get better jobs and pay more taxes, make better officers and enlisted members of the armed services, and contribute more materially, and in a wider variety of functions, to the strength and prosperity of the nation as a whole. With that understanding in mind, an eduction beyond those initial twelve to fourteen years provides significantly more benefit.
Some Disclaimers
2. "College" would mean any manner of advanced education beyond the twelfth grade, including technical or trade schools, as long as they are publicly governed. To be more specific, publicly-governed means a generally-elected or government-appointed board of chancellors; it does not mean privately owned or a corporation with publicly-traded stock.
3. I would encourage "free" post-grauate education as well, but only in return for a period of public service, no less than two years, in the armed services, Peace Corps, Conservation Corps, Forest Service, Park Service, Bureau of Land Management, or other government-run, non-sectarian service dedicated to the public good.