In other words, it's a market failure. Demand existed but the supply did not match it. According to neoclassical (and most other) economic theory, that shouldn't happen.
No, of course you can. Markets are supposed to adapt to changes in demand (and increase supply if physically possible), regardless of the source or reason for the demand. Otherwise, you're then admitting that markets are extremely brittle.
Let's consider another example. Consider that security situation of your country worsens and the government suddenly needs more grenades. So they start to buy them at expense of something else, like school lunches. Are you claiming that the market supply won't try to match the demand?
If it's true, then screw the free market. It's a bad economic system, if it can't do this. The problem is markets are treated as an article of faith rather than tools, so people don't want to admit their shortcomings.
> Although of course short-term, production is a zero sum proposition
I don't buy that.
> What should have government done, if it wanted to allow people get more education, and avoid the market failure?
Before, say, 1980, the US built the best university system in the world without government subsidy. After then, the universities became dependent on government subsidy, and the government began all sorts of regulations on them in exchange for the subsidy.
Before 1980, college was affordable. A student could pay for it with a full time summer job and a part time job after school. I know this because I did it.