Assuming the Kryptonian military was like our's, then physical one-on-one combat wouldn't be a big focus, but do we know enough about them to say either way?
There's also the difference between the institution and the man. Maybe it's unfair to say Zod's a good fighter because of his military experience, but that doesn't mean he wouldn't learn from somewhere.
Zod's gotta have something to balance things out and provide a high level challenge for Clark. Zod's supposed to be one of the rogues who makes Clark crap his pants a little because he's so dangerous and hard to defeat, and if Clark's got a lifetime of experience with his powers and the way they influence combat, then Zod has to have something to balance out that advantage or he's not nearly as much of a threat. I think Zod being a skilled fighter with a lot of natural talent provides that, and allows him to adapt to having powers quickly.
Totally agree about Faora too. I feel like she could be the Shiva of the Super-verse but everyone forgets she exists, or writes her as a henchman.