The question poses a historical assessment, and it requires a nuanced understanding of the successes and failures of Kublai, Hulagu, and Batu. Both Kublai and Hulagu are considered historical successes for the khanate for reasons outlined in option B—they were invaders who managed to gain the loyalty of those they conquered. Kublai, as the founder of the Yuan Dynasty in China, successfully integrated diverse cultures into his empire, showcasing a degree of administrative skill. Hulagu, on the other hand, established the Ilkhanate in Persia, achieving success in his campaigns.
Option C highlights Batu's failure in obtaining the title of Khan like his brothers Kublai and Hulagu. While it's true that Batu did not claim the title of Khan, the overall assessment of his leadership should consider other factors, such as the successful Mongol invasion of Russia mentioned in option A.
In a nuanced view, both loyalty gained and the attainment of the title Khan contribute to the historical success or failure of these leaders. Kublai and Hulagu were successful not only in conquering but in effectively governing their conquered territories. Batu, while achieving military successes, may be considered less successful in terms of establishing lasting rule or loyalty.