Some of the more basic very heavy spin sticks will do both lures and livies. I have a finor lethal 10-15kg rod that does both but ideal for neither style, another rod have used on kings successfully (including stick baits and poppers) is the older killwell jelly tip spin 10-15 kg. For large kings though where wanting to just  jig and live-bait, its hard to beat a heavy jig rod.

And here’s crux if I wanted to catch bigger kings and could take one rod, it wouldn’t be my stick bait rod, it would be a heavy jig overhead rod or preferably heavy jig spin set, for both livebaiting everywhere and jigging pins, …. and you can fish stick baits and poppers on the spin sets if you have to, have seen deckies (best example I’ve seen) on Pursuit  do it and catch 20kg plus kings. They can flick one out and retrieve one and once hooked up more power. Stickbaiting is bit like softbaiting, quite specialised. I like general fishing gear, but lot of jig rods are light have heaps of power, which is exactly what you need on decent kings and will fish heavier braid like pe 5 plus well..