Regarding the coming teacher shortage, one cannot discount the common practice of allowing teachers to retire on full pension after 30 years service, which results in them retiring in their early 50's, and puts the taxpayers on the hook for 35-40 years of monthly retirement checks and benefits. Without that absurd 30-year thing, the coming shortage would be nowhere near as challenging.
The fundamental problem with American public schools is that they are run by the Government. Accordingly, they are horribly inflexible, notably inefficient, and prone to creating perverse incentives that get in the way of accomplishment of the true mission which, one might note, is the imparting of useful information and nurturing well-adjusted, productive citizens. At that, they are conspicuously unsuccessful.
When I was a lad, I participated in a study of how different students learn. We were exposed to teaching workbooks, video lectures with teacher-assistants, and read-only learning, in addition to traditional classroom & homework. I never heard any results from this exercise, but obviously different kids learn in different ways. Could public schools do these assessments and create policies based on the results? Divide students according to learning style? I don't know.
I see no reason why exemplary teachers could not be employed to record classroom lectures, and those shown to students in a controlled environment, possibly with a Marine Drill Sergeant monitoring the process. Those videos could be used for multiple classes, schools, and even years. I'm talking about the best teachers here. But that would never happen with our teachers' unions standing in the way.