This discussion reminds me of an idea that I contemplate sometimes:
A mandate requiring that all teachers at the high school level or above have 5 years of work experience relating to the field they will teach.
Well, I became a teacher in my mid-thirties. Five years experience in my field was difficult because so few jobs are tied to an academic field. In a recession, that five years becomes even tougher to get. I guess you could say I did that, if you define my field very loosely, and include the graduate assistant work in university.
After I switched careers and became a teacher, I had to work in education for about 8 years before I got the chance to actually teach a class that was related to my undergraduate and graduate major fields (6th grade social studies, as it happens). Of course, about half of teachers leave the profession within their first five years, and teachers who are assigned outside their area of expertise are even more likely to leave. I'm still teaching because I am unusually stubborn.
Having been on both sides of the fence, I will say this. People in education have a tendency not to value education and experience outside of that field. People outside of the field of education really have little idea what is involved in education. But the real problem with your plan is that it is difficult to retain people who worked in another field before becoming a teacher, because people with experience and skills that are recognized by the world outside the school doors are less likely to be satisfied with the working conditions and pay of a teacher.
I have often had the opposite thought, that nobody should be allowed to enter a teacher training program until they have actually worked inside a K-12 school, even if it is just as a part-time Educational Assistant for a semester. But if we did that, I wonder if we might have an even tougher time staffing our classrooms.