Crack could mean many things, but not actually cracking it like a nut or summat
I suspect that the Earth Kingdom is not a single, unified state, but a mass of smaller, autonomous states that are historically associated with each other as a single cultural unit. The analogy drawn earlier to China makes sense here.
Consider that Bumi from "The King of Omashu" was quite clearly a king, but did not seem to be the monarch of the whole Earth Kingdom. My guess is that he's either one of many kings who may be under a single high king who could well be a relatively impotent sovereign. The only precedent that comes immediately to mind is the Irish Ard Ri, which doesn't match A:tLA's asian setting, but seems like a possible historical parallel.
I think the Fire Nations relative success may be owed to it being more organized and centralized than the other nations. The Air Nomads, as their name suggests, probably consisted of numerous small, spread out groups with the largest concentrations at the temples and perhaps traditional trademeet locations. The norther water tribe seems to be a strong, organized city state, hence its description by Zhao, but the southern tribe seems to be a collection of minor villages, provided it wasn't at one point like the northern tribe and then badly beaten by the fire nation.
One other thing that comes to mind is the status of the former Air Nomad lands. With the extermination of the Air Nomads, it seems likely that someone would have moved in to occupy that territory. Those lands may be occupied by the fire nation, settlers from the peoples, or some other group entirely.
I'm reasonably confident that the creators have this all worked out, they seem to have done rather well at their worldbuilding (does my conworlding heart good), but I would love to have a crack at the series bible for this show some day.
“What is earnest is not always true; on the contrary, error is often more earnest than truth.”