I think you just hit on something. Relevant degrees shouldn't be highly prized. If a teacher lacks the knowledge to teach a subject then they are not qualified to teach. When I was in college in the early 80's I watched mathematics majors become math ed majors when they couldn't deal with real math. I watched math ed majors become el ed majors when they couldn't deal with watered down math. A degree doesn't neccesarily qualify one to be a teacher. Teachers need a mastery of a subject. If you teach math in high school all that you need to master is the subject matter of what is being taught in high school math and the ability to teach. The subject matter in high school courses is nothing more than college freshman subject matter for non-education majors. That is unless you think remedial course work is freshman level work.
Bottom line: the knowledge required to teach high school is minimal compared to most other professional careers. A physics major, math major, engineering major, comp sci major and so on all have the required mathematical knowledge to teach math in high school. They get that knowledge by the time they enter college or by the end of their freshman year of college. This isn't rocket science. Rocket science requires knowledge well beyond what is taught in high school and undergraduate studies in college.
There was a time was a time when a college degree wasn't even required to teach K-12. Given the quality of education hasn't increased in America in the last 50 or so years, I contend that all of the additional degrees are a complete waste of money and the quality of teachers has decreased.
Well, there’s something in that. My niece teaches algebra to eighth graders, and barely had enough math courses to qualify as a math teacher. But because she is able to get the least promising eighth graders to learn algebra, she is highly valued by her school and district, and won teacher of the year for her district. I’ve probably forgotten more math than she knows, but I could never get anywhere with those kids.