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?

You can't compare Tolkien and the Matrix trilogy because one is a trilogy of books, the other a set of films. Secondly, I don't know who told you that the Matrix trilogy was supposed to contain a bunch of deep philosophy, but you were sadly misinformed. The Matrix trilogy sets out to be fun to watch and succeeds admirably. It relies on comic-book style and fast-paced action to do so. LOTR, on the other hand, relies on geeks filling in the characters' back-stories with encyclopaedic knowledge. Trust me, if you haven't read the books, there's not a ton of depth to the movies that's actually portrayed on-screen.

But anyway, if those are you examples of deep things in the LOTR, then there are five examples of depth practically in the first Matrix film alone. to wit:

a) At the start of the movie, Neo thinks that he is perceiving reality but it turns out he is not. How do we know that what we perceive is real?

b) Can the Oracle really predict the future if humans have free will?

c) Cypher's choice: would you rather live free outside the matrix eating gruel, or inside the matrix pretending to eat steak?

d) Agent Smith is an artificial form of life. What are the ethical considerations in dealing with him?

e) The humans and machines have a symbiotic relationship. How can we control technology without having it control us?