The typical phrase is “infantry wins battles, logistics wins wars.” It gets at the same idea as you.
https://www.czdefence.com/article/infantry-wins-battles-logi....
https://www.czdefence.com/article/infantry-wins-battles-logi....
This, mixed with the fact that Russia and the Middle East are thousands of miles away from the Mongolian and Chinese capitals made it inevitable that a leader on one side of the empire would ignore their overlord on the other side. Thus, the empire would fracture quickly (and pretty much did as soon as the family ties to Genghis Khan were loose enough).