I agree with your point about it being a cyclical problem, but have to disagree with the part about supply and demand. Much of what has to be taught in public schools is dictated by government policy (both state and federal). Art and music classes are typically some of the first things to be cut when there are budget constraints, so a surplus of those types of teachers leads to a surplus of unemployed teachers (or retraining for a different subject), not a surplus of those classes being offered.
"a surplus of those types of teachers leads to a surplus of unemployed teachers."
Yet, when budgets increase, these are the first to return, and the useful classes are never offered. I'm not arguing that art and music teachers end up unemployed first, but their existence is still what drives the lobbying for these programs. Government education policy (at the curriculum, not budget level), is substantially influenced by teachers unions.