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[Batu was Genghis’ GRANDson. My error. Mobility of leaders notwithstanding, the Mongol Empire had a single Great Kahn, who was infused with religious authority, which is a critical feature of the system. Next down the ladder were vassels of whom Batu is an example. There was no “atomization”.]

It certainly was atomized in the sense the aristocrats had their own armies. In a centralized state like China, the armies were on loan from the ruler, and anyone not the ruler who even attempted to stand up his own was guilty of sedition and faced the elimination of his entire family.

Whereas a Mongol aristocrat had his own army or war band by traditional right and often banded with fellow aristocrats or able commoners to fight or kill overbearing rulers. The Oirats who sacked the Chinese capital had numerous puppet rulers in the nominal titular role of Great Khan, but his powers were similar to those of Japanese puppet emperors who headed Japan for 8 centuries while shoguns wielded real authority derived from the troops under their direct command, killing any who failed to toe the line, albeit surreptitiously.

https://en.m.wikipedia.org/wiki/Northern_Yuan#Oirat_domination_(1388%E2%80%931478)
[In 1388, the Mongol throne was taken over by Jorightu Khan Yesüder, a descendant of Arik Böke (Tolui’s son), with the support of the Oirats. He abolished the Han-style title of former Yuan dynasty.[29][30][31] In the following year, one of Uskhal Khan’s subjects, Gunashiri, a descendant of Chagatai Khan, founded his own small state called Kara Del in Hami.[32]

The following century saw a succession of Genghisid rulers, many of whom were mere figureheads put on the throne by those warlords who happened to be the most powerful. From the end of the 14th century there appear designations such as “period of small kings” (Бага хаадын үе).[33] On one side stood the Western Mongols and on the other the Eastern Mongols. While the Oirats drew their khans from the descendants of Ariq Böke and other princes, Arugtai of the Asud supported the old Yuan khans of Kublaid descent. The House of Ogedei also briefly attempted to reunite the Mongols under their rule.]

In general, the fractiousness that provided Genghis, the scion of a minor tribe, to spread his wings also provided both cadet branches of Genghis’s descendants and talented non-related Mongols the opportunity to become noted war leaders and rulers at the expense of the official royal line. Without talented bureaucrats to prop up less talented rulers, and the division of lands from generation to generation, Mongol kingdoms became like the Rockefeller scions, numerous but not particularly powerful, and subject to being picked off.

What you describe is unlike what happened in the West. Perhaps you're reading Chinese histories that have a different bias? I wasn't there, and neither were you. What Western historians wrote down from the 15th century onward is well distilled in this excerpt from Kari:

The third era that influenced Russian thought in a great manner is Mongol Russia. In the 1200s, the Mongols conquered Russia. They held Russia for years. That time was cruel. There are a lot of words in Russian, related to torture, taxation, and corruption that come from the Mongol language. Dominance under personal authority was rooted in the administrative culture of the Mongols. That is, there is only one khan that leads. It is he who leads, no one else. Others are passive followers. That one guy leads and takes responsibility and the initiative. When the belief of divine legitimacy to lead is attached to this, the leader will appear fairly tough in their worldview.

The corruption and cruelty also come from the Mongol era. During Mongol rule, the only ways to survive were lying, corruption, and violence. This still lives very deep in Russia’s strategic culture. When Mongol rule ended, the Mongols did not just pack their bags and disappear from Russia. Instead, they mixed with the locals. So the traditions also stayed with the people. In particular, to the leading caste. The Mongols who had previously ruled the country merged into the ruling layers, which is still visible today.