Then there is the Khuzait faction cavalry movement bonus which is nonsense in the game environment, with the very artificial movement-party engagement mechanic. Khuzait parties can catch smaller lord parties and can evade similarly composed lord parties with ease. I'm against such boni/mali which affect game core features. No movement bonus (also not for Battanians), no autocalc cavalry bonus, neither in sieges nor on the field, no autocalc cavalry malus for sieges (as proposed by some).
The cavalry movespeed bonus is currently many times stronger than the Khuzait's culture bonus. The best you get with the latter is +0.3 on the map. Even the mounted infantry bonus is stronger by default. But the other reason for stuff like the cav bonus is because without it, the autocalc gives far different results from a live battle.
People think that the Khuzait bonus is way bigger than it is. Early on, it was implemented to give +10% on top of your total party speed. That meant taking a speed 6 party to 6.6, obviously a fairly massive increase. But it was re-coded to only give 10% to the Cavalry bonus, which tops out at +3.0 (flat), meaning the best you get is a tenth of that. And "the best" is pretty limited due to the Cavalry bonus being stealth debuffed by party size.
And your entire counterargument is... one failed state getting conquered, and furthermore, you use the entire conquest as an example (where other variables can come into play), rather than giving examples of individual battles (the only place efficiacy of crossbows/fortifications is actually relevant). What sort of testament is that?
My entire counterargument is that most historical people who fought (and defeated) nomadic cavalry didn't rely on crossbows paired with strong fortifications. Those were not an exceptionally strong counter because of operational limitations, not tactical flaws. That's my position.
We have a wealth of history (more than two invasions) to look towards to see that Chinese states, not only the Song, with inferior cavalry forces performed poorly relative to those states that could maintain strong cavalry forces, in the face of serious steppe confederations. Across those periods, crossbows experienced periods of waxing and waning military influence that were typically opposite the state's fortunes with access to nomadic cavalry.
As for why I use whole conquests and campaigns as my examples: because is standard methodology in the field? Because when discussing things broadly, you necessarily take a broad look at things. Especially when it comes to the interplay between weapons and outcomes, looking at events in isolation can produce a distorted understanding because almost every battle, movement or siege is shenanigans on one level or another. So the usual way is to look at trends.
For example of distortion produced by looking to individual actions:
But despite all this they held out with 8,000 soldiers at the Battle of Xiangyang against a besieging force of 100,000 for 6 years.
To put this into perspective, when the Song ventured outside their fortresses, they got annihilated, such as the multiple attempted relief forces for the siege of Xiangyang (which they sent piecemeal into a large enemy, like the incompetent idiots the Song leadership were). Why were the Song an easy opponent on the field but not in a fortification? Because the Mongols' traditional horse archer style just wasn't very good at dealing with sieges of stone fortifications.
This case is exceptional in almost every way. Xiangyang was carefully designed to be unsiegeable by 1268. It had massively thick walls, reinforced with clay and thick shrouds, with enough supplies gathered within to hold out for literal years. It was surrounded by a wide moat (more than 100 meters), ringed by mountainous terrain and secured on one flank by the Han River. We are talking the Dark Souls' Kalameet of fortification here and it came at a massive financial and resource investment.
The garrison inside the city itself was only 8,000 men but the Song repeatedly launched major campaigns to attempt to relieve it. For some reason, when Wikipedia mentions some of the losses incurred, it implies they were separate, disconnected and small scale actions. In reality, they were all part of Fan Wen-hu's summer campaign of 1271; his full force was described as 100,000 men, most of whom were killed in the process. They were not piecemeal attempts at relieving the siege, at least not primarily. The Song were certainly lacking in solid leadership but they weren't actually literally insane enough to believe a few thousand men could hope to break the fort and river investments.
But as for why this is a distortion? Because it wasn't the first time it had happened: Xiangyang also fell to the Mongols in 1236, in a matter of weeks.
That's why you don't look at individual actions when evaluating a claim as broad as yours.
(As an aside, I didn't mention the Persian siege engineers at Xiangyang in 1273 because the investment would have worked without them; the city was written off by 1272, the result of the failure of the summer 1271 relief campaign.)
At the time of the Mongol invasion, the Southern Song were not the "whole of China". They were about 1/4 of modern China's total area, while the Mongol Empire held roughly seven times the amount of territory they did. In addition, the Dali was attacking from the other side. I was only saying "five years" for illustrative purposes, but actually, the Han dynasty did conquer a similar area of China to the Song in nearly 5 years.
Yes, the Southern Song held less. They'd lost much to -- again -- some guys with horses who weren't the Mongols. I don't bring up the total land area because it is mostly irrelevant: income and population aren't equally distributed across land. The Yangtze River region, Lingshan and southeast held over seventy percent of the whole population of China (the geographic area, not only the Southern Song's territory) by 1200. It was an insanely fertile and productive stretch of land by standards of the time, unique anywhere in the world, and worth far more than a simply recounting of its total size would indicate.
Which Han conquest are you referring to?