It’s a vastly overdone story idea: What if Superman was actually a jerk. It’s also very unnecessary considering that you’ve got a Jerk Superman already built into the lore. That is exactly the best possible use for General Zod.
Zod is a great mirror to Clark. What if Superman was the type who saw his powers as something that places him over other people? What if he thought that violence was the best way to solve problems? What if you had a Might Makes Right Superman? That right there is General Zod.
And like Superman, Zod comes with a whole family of his own. His wife Ursa may not directly parallel Lois in any real way, but just being a superhuman like her husband is a contrast to Lois. I bet there’s a plot to be mined from Lois and Ursa having to team up to save their husbands or something. Lois could show her that brute force isn’t the only way. And Zod and Ursa’s son Lor-Zod is a natural foil to Jon Kent, Lois and Clark’s son, the current Superboy. Given the chance I’d find a way to have Jon and Lor-Zod going to school together.
The Eradicator has been teamed up with the House of Zod in recent years. It’s probably not how I would have done it, but even that can parallel the Superman family. These days Eradicator is Zod’s Steel (or maybe his Kelex?). And Zod’s other soldiers, like Non or Faora, are basically his equivalents to Conner and Kara and so on.
Nothing I’m saying here is extremely revelatory. Mostly I think the books get what to do with Zod and friends. They may not do it exactly how I want, but nobody is getting is exceptionally wrong either. Given control of the franchise, I’d probably keep them out of the Phantom Zone and give them a base on an asteroid or something. They could commute to Earth and to other planets regularly, without needing a thing about breaking out to begin each plot. Let’s just have them all around when we need them. If nothing else, maybe it’d allow writers to go to the “Superman-Turns-Bad” well quite so often.