OTOH, there are a lot of for-profit educational ventures, and they all seem really skeevy to me -- places like Kaplan or Phoenix University, for instance, or frankly a lot of educational software.

Perhaps a pro-market explanation is that the bureaucracy itself undermines the market, creating a market that is not truly driven by stated goals (education) but other factors. I'm not sure I believe that, but it's possible. The difficulty of procurement might in part mean that heavy up-front marketing costs dominate, and once you've made a sale it's both fairly large and neither increases nor decreases based on the quality of the product -- poor products tend to be maintained based on the commitment of the administration even when in practice they don't end up being useful.

It would be interesting if teachers were allocated money to purchase products themselves. While it seems somewhat chaotic, and challenging with student turnover (which is generally very high in the US in particular), it seems like the only way to actually have a market driven by real experience and taste rather than politics or theory.

I suggest you watch "Waiting for Superman" where they address the problems teachers face with being given merit based pay, which they could reinvest in product purchase. A quick solution for this is to create a localized version of craigslist specific to teachers where they can request donations of items/funds for specific projects. I tried to implement this many years back with a focus on computer donations, but the school administration shot it down because they feared the increase cost of their incompetent IT staff supporting multiple hardware formats, despite them often being nearly new technology. I did have teachers in Highschool who were able to build amazing labs based on applying for grants. Unfortunately these grants were not widely known about among teachers and they had no knowledge on how to write a good grant request. My HS physics lab actually exceeded the quality of the lab I used at university (UT at Austin). I was able to skip every literally single class, with exceptions of tests, and ended with a final score in the top 5% of the class.

The pro-market explanation in the case of University of Phoenix et al is that a lot of people want a degree to have the degree, rather than learn. Maybe they get a bump at work for having a master's.

So the market's working. Hence the term, "paper mills". It's much cheaper to sell people a degree than to teach them stuff.