WI: The Shun or Daxi took over China instead of the Qing

While we all know the Qing took over China after the Ming fell, what few people know is that there were two dynasties lying around during this period, the Shun, who were led by Li Zicheng and had taken over Beijing and large swathes of northern China prior to the Manchu Invasion, and the Daxi, led by the (infamous) Zhang Xianzhong, but what if either Shun or Daxi had taken over China? What would a China ruled by either one of those dynasties look like? How powerful would they be compared to the Qing IOTL?
 
Zheng Xianzhong was in no position to conquer China. However, Li Zicheng could have. Had Wu Sangui accepted Li as emperor or had Li defeated Wu and taken control of Shanihai Pass, the Manchus could have been repulsed. After that, the Shun would probably take just as long if not longer than the Manchus to take full control of China.
 
Zheng Xianzhong was in no position to conquer China.
Especially if the more lurid claims about him were true (that he massacred large swathes of Sichuan's population because they "made a secret pact with the enemy" (if the Jesuits there were to be believed) and erected the "Seven Kill" stele)
However, Li Zicheng could have. Had Wu Sangui accepted Li as emperor or had Li defeated Wu and taken control of Shanihai Pass, the Manchus could have been repulsed. After that, the Shun would probably take just as long if not longer than the Manchus to take full control of China.
Well, the reason why Li Zicheng didn't get Wu's loyalty was because he killed Wu's family and took his concubine, so, if he hadn't done that, Wu Sangui would have probably declared for Li Zicheng (like in this timeline).
 
Li Zicheng would have a multidecades long struggle ahead for his dynasty against both the Qing and the remnants of the Ming. The Daxi were probably not in position to take over all China, even if Zheng Xianzhong was not as evil as he is commonly portrayed to be.

Now what I find interesting is how the long-term success of Li Zicheng's Shun would be. Could they be a "gunpowder empire" which could suppress the Qing and Central Asians like the Dzunghars, or was dealing with the "barbarians" something only the Qing could do? How will the Shun deal with the Russians on the frontier, for instance? The Chinese being allowed to freely settle in a Manchuria which has been pacified by Shun armies is certainly pretty interesting.
 
While we all know the Qing took over China after the Ming fell, what few people know is that there were two dynasties lying around during this period, the Shun, who were led by Li Zicheng and had taken over Beijing and large swathes of northern China prior to the Manchu Invasion, and the Daxi, led by the (infamous) Zhang Xianzhong, but what if either Shun or Daxi had taken over China? What would a China ruled by either one of those dynasties look like? How powerful would they be compared to the Qing IOTL?
It would probably be smaller, more likely to remain in what has traditionally been China, unlike the Qing who conquered much of what were now call China.
 
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