Just so you know... Just because America has the strongest military in the world, doesn't mean it is of the best quality.
Being secretary of anything, means you'll be leading the entire department in its daily 'routine'. It doesn't literally involve being busy with the department's specialty all the time. Certainly, knowledge about what it does is certainly required, but you don't have to be as immersed as you claim you should be. Especially with the DoD. In military matters, that's what the generals are for. THEY decide what actually is done in the military, the SecDef is merely the political side of it and provides the frame the military can work within. To determine those, there is a legion of advisors. The SecDef just needs to be able to 'fix it' on the political side of it.
I agree that position like VA, Education and Public housing and Infrastructure are positions where extended knowledge is required, but that is also because there is a constant danger of career politicians/ government employees who DON'T change with the President/cabinet, that make decisions that only benefit themselves and not their sector. THEN you need a Secretary who can counter such assholes, because he has more/even knowledge liek them. That argument, however, doesn't really fly with DoD.