Yuan Chonghuan only commanded a fraction of troops in the Beijing area,and the emperor didn’t kill him out of pure paranoia either.Yuan Chonghuan legitimately broke the law by killing Mao Wenlong,who was of the same rank as he was, without any authorisation,and in doing so allowed the Manchus to get close to Beijing.
If the emperor wasn’t actually in Beijing itself,all forces in the region would have come under the command of a single person.
To say that Northern China’s solidly Han is a simplification of the picture.Northern China was ruled by foreigners for centuries.In many places,it had a strong tradition of Hans living next to non-Hans.Culturally,it was also vastly different to that of southern China.The literary tradition of the north for example has strongly regressed,with the Ming Dynasty needing to set up quotas for northern bureaucrats because the northern literary tradition was so bad that most northerners couldn’t pass the exams. For a lot of the northerners,it doesn’t really matter whether it’s a Han regime that’s ruling them or a barbarian one,as long as it could offer them security.