Hulagu (1217-1265), grandson of Genghis Khan, sixth son of Torre, founder of the Ilkhanate. He was originally Kublai Khan's brother, but after the establishment of the Yuan Empire, he did not return to the Central Plains until his death.
There are many reasons why Hulagu did not return to China, but to put it simply.

Blow the horn of the Western Expedition
In the second year of Emperor Yuanxianzong (1252), the Great Khan Möngke issued a call to Hulagu and began a western expedition. After this trip, Hulagu never returned. This powerful western expeditionary army first conquered Mulayi and then Baoda, and in 1260 Damascus was captured. At that time, the whole of West Asia was largely ruled by the Mongols.
Halfway homecoming
Hulagu, who occupied West Asia, was overjoyed when he heard bad news: Möngke Khan was killed in battle in Diaoyu City, and Kublai Khan, a brother of a milkman, and Ali Bu brother began to compete for the position of Great Khan. Hulagu, of course, sided with his brothers, so he mobilized his army to prepare for his return to the east. When Hulagu had just walked to Persia, the news of Kublai Khan's victory came, so Hulagu stayed behind, never to see his brother again.
Stabilization of the interior of West Asia
The main reason Hulagu remained in West Asia was to stabilize the situation here. The Mongols ruled in a rough manner, causing a large number of casualties and the destruction of the city, and the local resistance continued. In order to completely conquer West Asia, Hulagu needed to stay here.
Prevent foreign invasion
Don't look at the fact that in just a few years, Hulagu conquered West Asia, but surrounded by strong enemies. By the first year of the Yuan Dynasty (1264), Syria had been seized by the Egyptian dynasty, when Hulagu was preparing for the Crusade, but considering the golden Horde (Genghis Khan's eldest son Shuchiyi) was looking after the tiger, he had no choice but to stay and run Persia well.
Avoid suspicion
The Mongol tradition of infighting is too strong. They do not have a specific imperial succession system, and can only rely on fists. Kublai Khan came to power in this way, and at the same time he ascended the throne, he made his brother Hulegu the Great Khan of the Ilkhanate. The intention is obvious: run it there, don't come back. Hulagu, of course, knew the implications and gladly accepted the appointment.
Make a difference
It is certainly good to go back to China, but it is not impossible to go back to Persia. If Hulagu returned to China, he would at most be a prince and then be supervised by the emperor at all times. In Persia, Hulagu was the emperor here, so why not? Hulagu has a good historical evaluation, implemented a more tolerant policy in the local area, and accepted Islam.
Of course, another important reason why Hulagu did not return to China was that he died too early. In the second year of his reign as Great Khan, Hulagu died, but at the age of 49.
Finally, let's talk about this Ilkhanate, which is also called the Ilkhanate. Its pinnacle of territory stretched from the Amu Darya River to the east, the Arabian Sea to the south, the Mediterranean Sea to the west, and the Caucasus to the north, with the capital at present-day Tabriz, Iran. Although nominally part of the Mongol Empire and subject to the orders of emperor Dayuan, it maintained a high degree of independence. The status of the Ilkhanate is also very important, it ensures the smooth flow of the Silk Road, and its historical status is prominent.
In the thirteenth year, in 1353 AD, the Safi dynasty of Persia defeated the Ilkhanate and the khanate fell apart completely. Two years later, it was destroyed by the Golden Horde. The heyday of the Ilkhanate disappeared from the stage of history, thirteen years before the Mongols ended their rule in China.