I think the authors misunderstand the art of teaching in some fundamental ways. While discussing the many obstacles to entering the teaching profession mid-career, for example, they claim that courses on adolescent development or lesson planning are of "questionable value ore relevance to STEM education" and go on to suggest that mastery in one's subject area (in this case, engineering), is equatable to being qualified to teach.
The fact is, one needs to learn how to teach effectively. While having great command over your subject area is certainly important, a deep understanding of child or adolescent development and the tools of the trade (lesson planning, assessment techniques, educational technology) are equally important.
It seems to me that part of the problem is that people are attempting to fix education at a level higher than the school itself.
In other words, by adding regulation at a State or National level, you disregard the skill of the people running any particular school - the principal of the school and ancillary people in place to govern that single school.
I know one data point is not science, but serves to illustrate my point. My brother-in-law is a successful businessman to the degree that he no longer has to work, and mostly doesn't. His children go to a small, non US, school, which is autonomous. It is governed by a small school board (who do not govern other schools.) The board has accountability, but is largely autonomous.
So, one of the subjects the kids can take is Business related. He looks at the cariculum, and essentially volunteers to teach it. Of course being successful in business doesn't imply he can actually teach, but it really easy to find out, and guide him, improve him and so on.
He has enormous credibility with the students (since they all want to retire young as well) and he brings a wealth of information and experience to them which is not in the book. He might not be the perfect teacher, but if the kids WANT to learn from him, then he hardly needs to be.
This year he's piloting a program that will see all the high-schoolers (14 years old and up) start and run a real business. Real in the sense that they get investment from outside, by pitching to investors - real in the sense that they will be registered like any other business, pay taxes and so on. Not all will go on to be entrepreneurs, but any that do have all the skills before finishing high school.
Oh, and of course, he's only teaching a couple periods a day. It's the perfect marriage of skill, availability and willingness to pass it on. And it's only possible because the local school governance evaluated him, recognized the value, and we're able to creatively use that value.
It's impossible to replace all the teachers with people like him. And it's impossible to replicate him at other schools. Bt running a school is hard enough, without having them conform to some national ideal of what someone thinks every teacher should look like.
If we trust our principals, and local school committees, then ultimately they are motivated to do the best they can for the children, with whatever resources they have. Sure it's not fair, some schools will do better than others, but at least they can do the best with what they have.
Without national requirements we would end up with half a generation that has never been taught evolution as fact, and a lot who had to pay every day. Trust is only good when it is warranted.
I have two close friends who, right out of college, became teachers in California. Neither of them had teaching degrees; instead, they both started teaching with "emergency credentials" when that program was active. I really have no idea if they were good teachers, but they both seemed like they could be.
Within two years, both of them had independently concluded, "This job sucks", and they had returned to school to get advanced degrees within their initial field of study.
The thing is, they both loved the teaching part of teaching. Instead, they were both surprised at how much the paperwork and bureaucracy killed their spirits day after day. From their description, it was as bad as the worst Dilbertesque office drone position.
I guess setting up hoops to keep bad and under-qualified teachers out of schools is one way to go, but if your goal is to improve the quality of education, there needs to be focus on making the job a satisfying and attractive career choice. A lot of people think this means "throw money at the problem", but I honestly think, "minimize the non-teaching overhead part of teaching" would be just as effective.
The fact is, one needs to learn how to teach effectively. While having great command over your subject area is certainly important, a deep understanding of child or adolescent development and the tools of the trade (lesson planning, assessment techniques, educational technology) are equally important.