Why not? How does your normative point (that education should be free) relate to the positive point (that education isn't currently competitive) at all?
Also, I'm curious which service you believe should be free? Education, evaluation or credentialing?
Specifically, suppose we create a marketplace of for-profit education sellers as you suggest, and that marketplace creates good-enough-cheap-enough* slots for 80% of eligible students. What happens to the remaining 20% of students? In an ordinary marketplace, that demand would go unfilled, creating an incentive for more good-enough-cheap-enough slots to be created (up to some equilibrium, not necessarily enough for everyone). But we can't let "demand" go unfilled in this case (i.e., throw smart poor kids under the bus). So does the government fulfill its guarantee by favoring unacceptable sellers, either paying extra or lowering its standards -- giving sellers who charged less an incentive to raise their prices or provide a worse service? Or does it fulfill the guarantee by re-creating public universities, abandoning the goal of a for-profit marketplace?
These aren't rhetorical questions -- we're currently using both strategies, and more. It's not an unsolvable problem, but it's not a trivial one.
(Check out the Commonwealth Health Connector to see how Massachusetts is solving the same problem in health care, combining for-profit providers with a universal guarantee. They're not doing a bad job, but it sure ain't a conventional free market.)
* And then there's the question of what's good enough and cheap enough, when it's a democratic/lobbying process setting standards -- that's pretty different from an ordinary marketplace between lots of buyers and sellers.
Ultimately I believe the problem with what you propose is the idea that the government can guarantee that every buyer will find a seller at a (marginal to the seller) cost below X. This is just an attempt to pass a law against scarcity, which can't really work. All you can do with law is create different rationing mechanisms - perhaps replacing price with queues or favoritism.
Incidentally, even ignoring all government intervention, college education is not a conventional free market. Inefficiencies abound, most notably the prevalence of huge numbers of non-profit seeking agents and reputation effects.
For all those who like to discuss market failures, this is the place to find them.
Anyway: when pantaloons said "you can't have a competitive market for what should (ostensibly) be a free and universal service", they were making a normative claim that universal education is desirable, but a positive claim about how to achieve it: that "universal" and "competitive" are mutually exclusive qualities of any marketplace. That's the argument I was expanding on. I claim that it is very difficult to structure a competitive marketplace while also ensuring that everyone who needs some can get some. Thus if the goal is universal access to a good, affordable college education, your free market proposal is an incomplete strategy.
You seem to be saying that government cannot ensure that everyone has access to a good, affordable college education ("the government can['t] guarantee that every buyer will find a seller"). That's a position I think might be hard to support. The government absolutely can pass a law that prevents scarcity -- which is to say, ensure that citizens have access to something the free market doesn't make enough of. It can, for example, provide universal access to high school. It can provide universal access to assault rifles for healthy young men during a war. It can provide universal access to school lunch. It can provide universal access to health care for people over 65. It could, if it chose to make that a priority, provide universal access to college education for those who need it.
If you propose that "non-profit education is broken," and that the solution is for-profit education, then you need to either explain how for-profit education can provide universal access, or explain why universal access shouldn't be a goal.
The government absolutely can pass a law that prevents scarcity...
To some extent, yes. The government can redirect resources from other uses towards some fixed use. But the extent to which this is done is still fundamentally limited. For example, you can't significantly increase the amount of medical services provided for at least 7-8 years, which is the amount of time it takes to train a doctor. (You might, however, redistribute medical services from some people to others.)
Although I generally believe the burden of proof is on the people arguing in favor of taking action (e.g., ensuring "universal access"), I'll link to a post where I argue we should tax education rather than subsidize it: http://news.ycombinator.com/item?id=2454363
I didn't indicate that I think any should be free. I think education should be universally accessible.