What a old fashioned idea having pupils taught by people trained in the subject.
In some rural areas, that's not necessarily always possible.
One thing that would help is if teaching jobs were advertised and collected in a nationwide data base. There are places where there are shortages and other places with surpluses, but usually you have to contact each district to see what is open. Also, because of the pay structure and different state certification requirements, it is hard to relocate and stay in teaching. Most americans do move, but taching assumes one will stay put in one place.