On the topic of illogical career paths, Bones has a real job that requires being a very good auror, rather than being an errand-boy for Dumbledore, as Moody seems to be.

And as for "what are these people doing running a boarding school", they run a school based on reward and (mostly) punishment, rather than the growth of their pupils; they teach a rigid curriculum that seems to have remained unchanged for centuries, in spite of advances in both the magical and muggle worlds; and they socially condition people into narrow roles, largely defined by negative attitudes towards others, based solely on the House a piece of fabric sorts them into.