The rationale for Universal Free Public Education is that a certain level of education is necessary for a person to function as a full-fledged citizen in a well-tempered and thriving democratic society, lacking which any form of democracy is bound to fail, just as many democratic experiments lacking U.F.P.E. have failed in the past.
That is the sense in which in which it makes sense to use the word “free” in this context.
In that sense the reason for U.F.P.E. is much the same reason for prohibiting poll taxes. If being educated is part and parcel to being a citizen then there must be no obstruction to it.
U.F.P.E. becomes the right of each individual in a democratic society precisely because the society in question has come to see U.F.P.E. as necessary to its own survival and well-being.
The only question that remains has to do with the “certain level of education” that is needed for optimal functioning.
That level has shifted, mostly upward, through history. In the late Sixties when I left home for college, there was a general recognition that the future of our nation would depend on upping the notch a bit. California, being as forward thinking as they used to be back then, leapt ahead of the pack and inaugurated a First Year Free program for qualified high school graduates. Well, stuff happens. And Reagan happened. And that was the end of that. And the country has been going backward, education-wise, well, not so wise, ever since.