Lots of alternate history timelines focus on the Mongols, so any analysis of Mongol decline is important to understand what might have been. This paper says the political tension between Kubilai Khan and the Ilkhan are to do with Chinese and Persian influences as the Mongols went native.

The Ilkhanate was "barely a coherent state" and was seen as dubiously legitimate in Chingissid terms, and its conversion to Islam weakened the Ilkhanate by undermining the ideology supporting a centralised state. The same thing would have happened in Europe because of similar tensions between the church and state.

https://www.academia.edu/26388293/Th...l_world_empire

The Ilkhan Sultan Öljeitü died on 30 Ramadan 716/16 December 1316; it was not until early–mid 717/1317, several months later, that his only surviving son and designated heir, Abū Saʿīd, was enthroned in Tabriz. It is true that at the time of his father’s death, Abū Saʿīd was in Khurasan, and that he was only 12 years old. Nevertheless, the delay suggests quite strongly that the senior noyans— notably the amirs Sevïnch and Chūpān—were in no great hurry to maintain the unbroken continuity of Ilkhanid dynastic rule, and that the anxiety nor-mally attendant on the absence of a ruler—leaving the kingdom rudderless and prey to the ambitions of men of violence—had evaporated. We might rephrase this to say, the anxiety ‘normally’ felt by the bureaucratic classes and their historian mouthpieces; the men of violence were evidently less alarmed at the absence of a restraining authority. As is well known, the lack of con-sensus surrounding Abū Saʿīd’s accession found a resolution only after the so-called ‘revolt of the amirs’ in 719/1319, when Abū Saʿīd won his spurs but at the same time was obliged to accept the tutelage of Amir Chūpān.