I'm just going to debate on this just out of curiosity. Lets start with the 6 to 9 support personal for one soldier ratio, isn't that a modern era phenomenon? For instance, the Iraq War era US military's combat soldier is supported by 8.1 support personal while a WW1 US soldier is supported by 2.6 personal. However, during the US Civil War, if I remember correctly, a single blacksmith can support up to 30 plus soldiers. I can imagine that the ratio/ tooth to tail is even more lopsided in favor of combat personal during the ancient times. Plus the conscripts were just minimially trained peasants who just lived off the land, and their mass destruction can explain why the Zhao never recovered and basically became a zombie state after that defeat.
In your counting of morden wars, you did not count the menhours building those weapons and farmers who produced food for the soldiers in the years of the war, did you? If you count them in and compare with the past, you would get that the ratio in acient time is higher. The whole war is a systematic machine that every bolts and nuts have to be counted to enable the war.
The difference between acient time and today is the
efficiency (due to technology advance) of material production and transportation. To illustrate, in acient time, a farmer can only produce surplus for 3 men (blacksmith to make weapon and 2 soliders to fight). A morden American farmer can feed a lot more people in the city, I read somewhere 8 people. Transporting food to the battle field need one man and many horses 10 days during which most of the food were eaten by the transporting man and his horses. Only about 1/3 is left for soldiers. In morden time a truck in a single day can do the job of 10 horses in 10 days. The logistic cost is the gas which is also produced in high efficiency. These non-combat logistic cost is much higher in portion in the past.
One trick that historian used to exagerate the war-god like Xiangyu is to count only the soldier in the battle field, but counting all transporters and drafted civilian with a stick from the opposing side. In reality the number of real regular soldiers on both sides aren't as different as the story said. For example, the PLA paper gave the true number being a fraction of the quoated number from Shiji, I believe the PLA paper is closer to the reality.
One can suggest that such horses did exist but most were subsequently wiped out during the Chu-Han contention. That is why the Western Han needed to explore for horses.
Horses live and die. Western Han greatly increased population, so were the horse population. I don't think Chu-Han contention period is misteriously more able to breed more horses, especially when it followed the Qin's short time of "peace" after the unification to recover from the warring state' hundreds years of war which would have already "wiped out" horses.
Note that such a time gap is huge and numerous wars occurred. You would have to factor in a time gap between the Chu-Han contention and the Qing, which is almost 2000 years.
The climate and size of grazing land did not change much during that 2000 years in northern China, Mongolia and Manchuria, nor was there any more advanced breeding method. So I don't see a reason of the time gap making a difference.
A good example is the crop production rate (per unit area) did not change much over thousands of years. The only change happened when new tools were introduced, namely from stone/wood to metal tools or new crop breed. Between such change, nothing changes.
Another example is China's population, before Song dynasty China's population was 60 million at its peak, this number reached about 150 million in Song dynasty due to the development of algricuture land in southern China. It remained so mid Qing then jumped to 400 million due to the introduction of corn from America. The increases only happened when new land (Song and Qing) and/or method/tech (corn) were introduced. These factors did not happen to horse breeding though.
