Interestingly, the idea that Europe was wide open to invasion and almost miraculously saved by the great Khan's death is still out there among historians. I just read an article written in 1997 that took that position. Like you, however, I find this argument pretty weak, given that it is based on too many assumptions. The fact that the Mongols could defeat European armies, does not necessarily mean that they could have conquered, let alone held, large sections of western Europe. And since they never actually tried, we really have no idea what might have happened.
Actually, the real reason that the Golden Horde withdrew was kind of complex.
Apparently, Batu and Subotai were really at odds at each other. At their victory feast over the Hungarians, the commander of the European conquest was supposed to have the first drink from the horn. Batu assumed that it was himself, but his brother Shiban refrained from letting him drink first, saying that the honour was Subotai's. Batu threw a huge fit over all of this. This seems to imply that the real commander and brains behind the whole operation was actually Subotai, even though Batu was officially declared "in charge".
Then, Ogedai Khan drank himself to death. He was known for being a
bad alcoholic. His brothers tried to talk him into drinking less than three glasses of wine a day. Ogedai conveniently avoided this by drinking from unusually
large glasses.
When he died on December 11, 1241, Batu was quickly informed and he wanted to stake his claim for the election of the next Khakhan. And since he was already at odds with Subotai, he decided to withdraw his own forces with him back to Mongolia. Subotai's army shrunk nearly 35%.
Then, as Mattheu of Paris informs us, Frederick II(Stupor Mundi) of the Holy Roman Empire and St. Louis IX of France had made the crusader's oaths to retake and liberate Central Europe. It was going to take time, because Frederick's forces had been exhausted from fighting the Pope in Rome, and Louis' forces had shrunk from the wars against England. Therefore, word was sent all across the Western world, to repel the Mongols was going to take a massive force and they would need every volunteer they could get. Men from as far as Norway, Ireland, Spain, and Sicily were making the crusader oaths to depart to Central Europe and fight the Mongols back into Russia. Mattheu also says that since Frederick was too old to do battle himself, he was going to send his ingenious (and also illegitimate) son, Enzio of Sardinia, to lead his army against the "Tartars".
Louis IX, still a young headstrong man, and also quite pious, was asked by his mother, "What shall you do against the Tartars in battle?"
He replied, "We shall send them back to Hell from whence they came."
Then his mother asked, "What if it is they who defeat you?"
Louis replied, "Then they shall send us to Paradise!"
All of his men laughed and at that moment were psychologically relaxed enough to resume stockpiling the weapons and supplies needed for the expedition.
Then, when news reached the Europeans that the Mongols had withdrawn in the winter of 1242, the whole crusade was cancelled.
Subotai took his forces out of Hungary and Poland and withdrew into Russia, with some quick stops in Dalmatia and Bulgaria to pick up some more loot. Since Subotai knew of the coming invasion from the West, and had no reinforcements to back him up, he probably assumed that there was no way he could conquer Europe if the West was going to unite to repel him and so just gathered up enough plunder to justify the invasion.
But, in the one year the Mongols spent in Hungary, over 75% of the Hungarian people had been exterminated. When King Bela returned, he had to invite the nearby nomad tribes of Cumans and Pechenegs to settle on Hungarian land in order to repopulate the country.
Certainly, this horrible war which lasted only a year still rings in the minds of the Polish, Bohemian, and Hungarian people to this day. If the Mongols had continued to attack into Europe and the crusade had been fought, there would have been a lot more bloodshed than would have been necessary.
So, the whole invasion of Europe was one major bloodbath which began in earnest but ended up going nowhere for either side. Just imagine how history would have changed if the Mongols won!
Some food for thought,
Justin
A man believes what he wants to believe. - Cuchulainn