Even if we would accept that their bows were better then some other steppe peoples, he still thought many people that for sure had the same bows as he did.
In fact, most of his life, he thought people who had the same technology, including the invasion of the Qara Khitai.
Then the Jin had allies that likely had the same bow technology. However it seems most of those allies just switched sides.
Only the Khwarazmian Empire and Xia likely didn't have significant troops armed the same way.
His great accomplishment was marrying that with the ability to besiege walled cities. Nobody expected barbarian horse archers to be able to do that.
https://www.nationalgeographic.com/science/article/140310-ge...
In terms of numbers, it's entirely possible that larger numbers of defending sedentary soldiers are needed than attacking horse-riding nomad soldiers for the former to mount an effective defense against the latter.