That would be an effective tactic for suppressing the partisans; I'm not saying it wouldn't. But the anti-partisan sweeps would take a very long time to have a significant effect, and would require Siwan Khan to dedicate a large percentage of his total army to rear area security... which is about as much as you can hope for from partisan operations in any event.
The best partisans will either disrupt logistics or prod the enemy into pulling back a lot of troops back to stop them. They're not going to defeat an entire army by themselves or anything, and it would be unreasonable to expect them to.
But by the same token, I don't think it's reasonable to assume that Siwan's Kharash tactics will have been as effective as the average armchair strategist might think at eliminating the partisan threat.
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That said, Siwan Khan appears to be doing it for a different reason. It might be a practical solution to the partisan problem (if not a 100% effective one); I'm not sure. But in a modern context, it doesn't make as much sense as it did in the 12th century.
So I think a big part of the reason is simply that Siwan is a brute. He sees no problem with doing this, and is probably pleased to do it. The long-term consequences aren't going to be the same as they were when Fu tried it back in his salad days.
I strongly suspect that this one had a double intent. Being crushed alive may be an honorable death in Mongol eyes, but I'm sure the Mongols involved knew quite well that it was an extremely painful and unpleasant way to die. And sitting on them while they expire doesn't strike me as necessary for the honor of the thing.
Thus, crushing Russian princes most likely served a double purpose. On the one hand, it was an honorable way to kill off a troublesome enemy ruler in Mongol culture, thus satisfying the Mongols that they had shown respect to their defeated enemy. On the other hand, it sends a message to all potential troublemakers: "continue to make trouble and we will kill you slowly and painfully in a way you would never have imagined before." As opposed to "make trouble and we will give you an honorable death."
As you say, the Mongols were very competent. It seems likely that they knew quite well what kind of psychological effect some of their actions would have on the foreigners they conquered.
That was my point, the Kharash concept is wholly inappropriate in a modern war.
They definitely weren't a modern army. They were however very fierce fighters, accustomed to immense hardships, superb horsemen and had long traditions of warfare. What set them apart from the run of the mill steppe warrior who is also a fierce fighter, good horseman and acustomed to hardship is that they were very disciplined (the average steppe warrior hates having to follow orders), very motivated (the average steppe warrior, when not defending his tribe, is only interested in quick booty and loses interest in fighting quickly when faced with difficulty) and above all led by brilliant leaders who knew how to lead large armies and who could get skilled foreigners to help them whenever native Mongol talent did not suffice. (f.ex. siege engineers)
When I say they were a modern army, I don't mean that they had rifles. What they had was a very sophisticated signaling system, a combined arms mentality, and the ability to move faster than any other army on Earth before the arrival of tanks.
When you list the differences between the mongols and the average steppe warrior, you act like these traits are somehow typical for other 12th century armies. Having all loot and booty allotted after the battle by a central authority is different from every other army of the time. Using captured enemy weapons against other enemies, merit based promotion, extensive intelligence operations and reconnaissance, these would not become standard in Europe until the late 1700's. That was the great innovation of Genghis Khan, take warriors who are already skilled and then organize them like a modern army.