Ultimately, they were still just a couple of unruly bandits who had gotten too much power that its officially recognized by the state.
This was never really true, considering Kan Ki conquered bandit clans and ammased his own armies in the thousands. At that scale of organisation, they were no longer really bandits anymore. They were an army without a nation to serve.
Method of operations for renegades (bandits, rebels, terrorists, etc.) are going to be much different from those who progressed through standard military ranks. He's most likely to be much more proficient in unorthodox methods of warfare, including psychological warfare (deception, scare tactics, stealth operations, subversion of Kingdom's own "Geneva Convention", and thus even when commanding larger number of soldiers, his primary strategy during a battle is usually going to be based around those four tactics.
He's literally the ancient China's embodiment of "What if a career terrorist became a Four-Star General?"
Different skills and disciplines are involved, but there will be significant operational overlap when commanding tens of thousands of men.
Kan Ki also wasn't a stranger to conducting open field combat and sieges, which require strategising
I don’t think Kyoukai learned strategy. I think she made up her own strategies just like Kanki did, based on her assassin training. I don’t want to defend Kyoukai because she is the definition of mid but I was always fine with her limited strategic knowledge.
Kyou Kai absolutely learned strategy, and was quickly putting that into practice in command of her own unit. Not only did her acumen quickly develop to anticipating Ka Ryo Ten's orders, she was the first to comprehend Ou Sen's Locust stratagem, and also the one that suggested their winning strategy for taking Nanyou. Her strategic acumen is real undeniable.
Strategy is a discipline first and foremost, not a knowledgebase.
The big thing to realize about “Kanki’s weakness” is that Riboku was incorrect about his weakness and the manga acknowledges this. Kanki broke out of Riboku’s encirclement because Riboku was wrong about Kanki being able to be checkmated by traditional warfare.
It only partially invalidated Ri Boku's prediction on Kan Ki's weakness. He was still, evidently, correct about Kan Ki simply not knowing conventional strategy and tactics.
hy would he be capable of traditional military tactics when he was never taught them lol
I laid it about pretty clearly: because he was a genius of warfare with all the access and opportunity in the world to learn, whether he was trying to or not.
You'd also think he'd learn a thing or two from beating the armies that were sent after him prior to Mou Gou.