I don't see what this has to do with the hiring process, but in response I can say that you're speaking to an institutional difference. At my undergraduate institution most of the mathematics majors aimed to be middle or high school teachers (and now are), and their education was supposedly geared toward that. I say supposedly because the "education track" had lower standards and easier requirements than the other tracks (applied and pure math). So they might not be the same people you call "competent."
Moreover, most of the professors at my institution came from industry. They also did not originally aim for teaching, but switched into it. Many of them happen to have a PhD, but there is no research at my college (it's a polytechnic institute). If high school teachers had the same level of respect and comparable pay (and were similarly sought after), I see no reason why this couldn't also occur in high schools. We do, after all, see so many articles on HN about how there aren't enough jobs for our graduates.
Then I think we agree on what the solution may be- getting the same level of professional respect. I think one way to do this is to make it a full-time, year-round profession.
Unfortunately, I'm afraid that this might severely cripple the people who entered the profession because of its' family-friendly schedule.
I'm glad to hear that most of the mathematics majors at your undergrad institution were intending to be teachers. That gives me some hope.
[Specifically, I was responding to the 'hire for one year with oversight' bit.]
I see a cultural basis for some of the problem. Money is a huge factor. But if you are going to give more money, you're going to want to demand more. Some of the teachers in place now aren't particularly competent. By making it a more demanding profession perhaps we can get more people who want to do it for love of a subject rather than convenient hours.
Moreover, most of the professors at my institution came from industry. They also did not originally aim for teaching, but switched into it. Many of them happen to have a PhD, but there is no research at my college (it's a polytechnic institute). If high school teachers had the same level of respect and comparable pay (and were similarly sought after), I see no reason why this couldn't also occur in high schools. We do, after all, see so many articles on HN about how there aren't enough jobs for our graduates.