>Combined arms was a concept understood at the time (Ming Dynasty in this 17th century battle) and had been used since the 400s BC (when crossbowmen were combined with archers, pikemen, halberdiers, etc in Warring States armies). The Ming Dynasty had pike formations that combined musketeers with pikemen and archers.

Military tactics and theory were not directly passed down throughout Chinese history. Many things related to mathematics, science, engineering, military strategy etc. were either rediscovered or reinvented hundreds of years later or not even known that the Chinese possessed such knowledge till the 20th century until studies by Sino Scholars. So just because there is an example from BC's, doesn't mean it was still actively analyzed in AD.

And the reason I said the Ming had no concept of combined arms was I meant they had no idea how to use musketeers and artillery with their infantry and cavalry. So firearms weren't very effective, which is why the Chinese never fully invested them in as opposed to the Japanese and Europeans who saw the huge advantage that firearms had and basically equipped their entire armies with. The Japanese actually used massed rotating volley fire combined with infantry and cavalry support to resist charges and push back against the enemy. The musketeers were used like how Napoleon used artillery and cavalry together. Break up the formation of the enemy with withering firepower and charge in with cavalry backed up by infantry. The Ming were defeated in almost every pitched battle against the Japanese in Korea and only pushed through due to the Japanese running out of supplies or retreating when in danger of being isolated by the Ming and Joseon forces. So yea, maybe some Chinese strategists were aware and implemented such tactics but clearly those ideas were not spread to the entire Ming military nor became uniform tactical theory across the country.

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>The 16th century Ming general Qi Jiguang even developed a quasi-pike formation called the Mandarin duck that combined shielded swordsmen + pikemen + ranged troops (muskets, archers, etc) + a guy with a weird polearm called the wolf's brush.

You're talking about the polearm that was like a bamboo branch that basically shoved in the enemy's face right? I've heard of this too but I'm assuming it was that one general's tactic and no one else used it. And it seems he mostly used it against Japanese pirates and rebels in the South. No idea how it would have fared against the Manchus or actual Japanese military units.