I listened to an audiobook, the Great Courses Plus, that claimed that the Western/Formal Han dynasty in the western area of their empire had a more centralized government (including the capital) with commanderies but in the eastern portion they allowed semi-autonomous rule with kings. With this narrative and kings being a potential threat, why in the world would they allow kings to rule in the first place, when they very well could have expanded their centralized government?
Somebody on this sub might be able to answer your question with more updated details but I can give you an answer from Wondrium (Formerly The Great Course Plus) "Understanding Imperial China" by Andrew Wilson and the reasonings of the Han historian Sima Qian.
The main source are Sima Qian "Records of the Grand Historian" written with the author bias, but still a comprehensive primary source.
According to Sunzi, "Art of War", the spoils after the conquest should be distributed to soldiers based on merit. It is standard practice. The Zhou dynasty founder reward his advisor Jiang Ziya with fief of his own and name him duke. The Zhou kings continued rewarding meritous officials and generals with fiefs and titles for the following centuries weakened their power and lead to the seven warring kingdoms which each rulers called himself kings. When the Qin king united the land, he concentrated all rulings into himself, determine not to repeat the previous dynasty mistakes.
Qin brought peace and tyranny. Strict laws and severe punishments were forced on the people. After the first emperor died, peasant rebellions and former nobles ended the unification in relatively short time. The warlord most responsible for the Qin fall is XiangYu, an aristocrat general of Chu who became the head of the alliance, divided the lands amongst his subordinate generals into 18 kingdoms and name himself Hegemon King. One of the subordinate, Liu Bang, was given an isolated land and the title of King of Han.
Liu Bang was a commoner, beloved by the common people. During the rebellions, the emperor of Chu, the alliance nominal leader, sent the armies Liu Bang and Xiang Yu to attack the Guanzhong (Qin kingdom territories inside the defensible valley). In efforts to divide the two leaders, he declared that amongst the two of them, whomever took the Qin capital first will be named King of Guanzhong. Liu Bang, reached the capital first, but Xiang Yu ignored his master' s declaration. Liu Bang was, in effect, banished and given a reward far from promise, and his family were held in hostage.
In exile, he acquired the service of Han Xin, an underused subordinate of Xiang Yu, who said ".. But when someone he (Xiang Yu) has sent upon a mission has achieved merit and deserves to be honored and enfeoffed he will fiddle with the seal of investiture until it crumbles in his hand .." Several of the 18 states rebelled against Xiang Yu in the east. While Xiang Yu were there to crush the rebellions, Liu Bang and Han Xin attacked on the west beginning the Chu-Han war. During the war, many kingdoms changed sides, and punitive actions had to be taken against them. Many of the former rulers and the kingdoms were absorbed in the process. Han Xin, not always a good subordinate, was given the title as a king to ensure his service. To gain his final victory, Liu Bang had to convince two other kings serving Xiang Yu, Peng Yue and Qing Bu, to defect to him. Liu Bang, the King of Han, got the title as emperor and the armies that were raised on the rebellions were disbanded.
As you can see, to gain supreme authority, he had to attain the help of vassal kings. After he became emperor, on the advice of Zhang Liang, he also give titles and lands to officers he hated so that they would not rebelled. Later, Liu Bang made the families of the new aristocrats to reside close inside his territoties. This weaken them. He, or his wife acting on her own, also executed kings who helped him into power: Han Xin, Peng Yue and Qing Bu. In his deathbed, he made his officials swore an oath that the title of King cannot be given to anyone not surname "Liu".
It is so that what happened to Zhou kings and Xiang Yu cannot happened to his family. However, the Qin centralization model led to their downfall and the rise of Han. The Han model is a hybrid of the two, prefering the peace but not the Qin actions that brought its downfall. Liu Bang, last act, also protected his family from destruction by his wife who took power over the court and raise the authority of her "Lü" clan over the "Liu". After her death, one of Liu Bang childrens, the King of Dai was made emperor. His brothers and cousins were also kings in their own rights with their own territories who can challenged the emperor if united.
In the reign of Emperor Wu, his official Zhufu Yan, proposed a law guarenteeing the emperor from further powergrap. The law decreed that each vassal kings had to divide his inheritance amongst his children. With this, no vassal kingdom can retain its shape and its ruler cannot grew strong enough to challenge the emperor authority.
In summary, the Han emperor need the supports of the vassal kings to become emperor. They are not keen on centralizing everything which is the leading cause the predecessor' s downfall nor was to weaken their authority by awarding kingships, unless for their close family. After Zhufu Yan, proposal, the emperor is secured from threats except for those that came from centralization. In the end of the Eastern Han dynasty, the government ineffective rulings forced them to allow regional governors to raise their own armies. They were able to pass down their armies and other authorities to their principal heir undivided, and the Han dynasty ended.