You’re missing a key point here: Management is a secondary function, in the sense that management doesn’t in itself produce anything of value. When done correctly, it enhances the productivity of those actually producing something.

In order to be effective at management, you need to have a good idea of what the people you are managing do. Otherwise, you won’t be able to appropriately manage resources and help people be effective by moving support to the right places. “Management” as a degree aims to teach people how to manage resources they don’t understand, and more often than not ends up producing managers that have no idea what the engineers and technicians they’re managing actually do. These managers are usually more of a burden on the people they’re managing than anything else. Every good or decent manager or leader I’ve come across has a background from the field of the people they’re managing.