This was partly to get away from the Mongols and their massacring, but that noted, the Mongols were comparatively light rulers. They were happy to live in their yurts and collect tribute from the ever-bickering Russian princes, and all the princes had to do in exchange for their relative freedom was recognize the Mongol khans as their rulers and allow the Mongols to pick the Grand Prince from among the Russians. Perhaps most importantly, Mongol rule cut the Russians off from the Byzantines and further isolated them from Europe, leaving Russia not Byzantine, not European, and not really Mongol either, since they hated the Mongols and generally believed that the Mongols were a scourge sent from God to punish them for their sinfulness and everything. But the Mongols did help propel Moscow to prominence, and in doing so, created the idea that this was Russia. And as an aside, they also did what Napoleon, Hitler, and many others couldn't. The Mongols successfully conquered Russia in the winter. Thanks, Thought Bubble.