This suggests to me that there could be a marketplace solution to the problem...
There is a marketplace solution to the problem. It's called government funding. Education as a market good has a ton of positive externalities attached to it. If little Timmy purchases an education for himself, he benefits in the form of increased earning potential, but everyone around him benefits as well: his employers receive a better employee, his employees receive a more profitable workplace, and his fellow citizens receive a better informed voter. Since these benefits are non-excludable -- there's no way for me to pay for part of Timmy's education and have it benefit only me -- the most fair way to pay for these positive externalities is through public funds.
My Libertarian leanings would prefer to see less Governmental influence in education.
Because you want the market to underproduce education, or because you want the taxpayers to subsidize this public good while having no say in directing their expenditures?