Its seems your putting too much emphasis on only just programming and implementation. sure a high school er can get a programming job but when it comes down to real software engineering that's a different story. You need lots and lots of math to work as a software engineer, So a Computer Science degree or Software Engineering degree is worth doing and is pretty much mandatory for Engineering positions. Math and physics majors can get Engineering jobs too. It has to be STEM or computing related degree. Software Engineer's Plan, analyze software requirements, specify and document the requirements, design the software system and then pass it down to the programmers to implement and code the software.