Let me try again. My main point was what someone studied at 18-21 may be irrelevant by the time they come to an important job twenty or thirty years later. It is quite possible for someone with a non technical/scientific degree to gain experience and professional qualifications later.
I am all in favour of people who know what they are doing running things. Most management tasks require teams of people with different skills. The Leader needs leaders skills, which are more about choosing talented and qualified people, incentivising them, establishing correct accountabilities, setting targets and making ultimate decisions where need arises. The team may need a scientist, a technician, a stats and maths analyst, an engineer etc.
Having a relevant degree at 21 does not mean you can run something 20 years later. Someone without a relevant degree who is good at choosing people and leading may do well as they gain management experience.
If you are a professional you have to take exams. Equally important you need to keep up to date and keep practising as experience and evolution of knowledge matters. Medics, lawyers, finance professionals etc do this through Continuous professional development learning and testing sessions. I was certainly not proposing seeking medical advice from a non qualified person, but would be happy to see a Dr at a clinic or hospital run by a good manager whatever their degree. I took a professional qualification later in life and keep up to date on investment and economic issues daily.