That was the path I followed in physics, though I took a bit longer to finish. I had friends in fields (e.g., psychology) where they had to do an interim masters. In my view, the result was that the masters became a hoop to jump through, and one that saddled the literature with studies that weren't really very meaty.
Personally, I'm leery of anything that makes the degree take longer. The reason is that grad students face the constant risk of things that can force them to quit without anything to show for it. For instance your advisor can spontaneously quit, or for that matter, drop dead. Your research can get "scooped." You can run into health or family issues.
>>> Most professors are not trained teachers.
Most college teachers are not professors. A few years ago, I taught a couple of college courses for a semester. If you want things like teacher training, then you have to make college teaching remotely career-worthy.
I will say that I have had some discussions with PhD admissions faculty and they say that it is very hard to select which undergrad students to accept PhD programs. Essentially none of the metrics they have -- GPA, GRE scores, courses taken, etc -- have any predictive power for how "good" of a researcher a given student will be. Perhaps if they had to do a masters first it would help.