Why such an extreme "solution", when instead you can attempt to generally lower the tuition fee somewhat, to make it affordable AND remunerative? I can imagine a "free education" will come at a (high) cost for something else. Or is it the kind of "free", where added expenses aren't mentioned yet, like hidden airline charges?
There are many "hidden fees" supplies, activity fees, field trip fees, lunch tickets, breakfast tickets, maybe a bus fee or there may be a fee. That's assuming it's a public school, and not a private one. Now there are low income programs to help cover the cost of many of those fees if the child comes from an under income family. (I say under income because not because it's a PC word to say poverty because the program has different definitions for what the family gets charged based on income so a family may not fall under the poverty line and may qualify for free or reduced cost meals.)
So not really "free" but at very low cost.
I actually wasn't even taking these kinds of supplies into account, as I tend to associate the word "education" with College. However, in NL we have this problem of grade school teachers having to buy learning material (intended for arts and crafts/decoration, but I think I've seen this includes writing supplies as well) from their own paychecks, being unable to declare the money they've spent. So as you said, "nothing is free".