Who has summoned me from slumber? What mortal has dared disturb my hangover.

Ok on the Shahnameh my knowledge is a bit limited. However there does have appear to have been a sudden surge in production of illustrated Shahmaneh during the Mongol period. Indeed 1/3 of surviving illustrated texts from the period 1280-1350 are Shahmaneh, furthermore Shahmaneh's from this period represent the earliest known illustrated copies. This production would almost certainly have benefited from Mongol patronage, Persian art of the period benefited substantially from the Mongol presence. I could further speculate about possible use of the text as a tool of legitimisation but I lack enough sources to do so and so am not allowed to do that here.

However while it appears the Mongols actively encouraged interest in this text that is a central part of Persian culture this should not be seen as a return to old pre-Arab styles. The Mongol presence brought in motifs from other areas they conquered and came into contact with. So in Persian paintings we see landscapes painted in Chinese styles. Another good example is the Universal History/Compendium of chronicles which was compiled by Rashid al-Din, a Persian serving as a government minister for the Mongols. This manuscript was rather beautifully illustrated, and we can see a wide variety of styles influencing the art such as Buddhist, Siennese Italian, Chinese and Byznantine iconography. If you look at this and this, both from 1314 copies of the work, you can see that the illustrations have some rather Chinese influences. These manuscripts would would have been illuminated in government workshops in Tabriz which had artists from across the Empire working in them.

Could you expand the argument a little bit? I can't tell whether you're referring to the Abu S'aid version or the Muhgal one.