If the Romans had conquered all of Persia, Bactria, and Xinjiang, and were sending periodic raids down into the Gansu corridor then your analogy might make sens

If the Romans had conquered all of Persia, Bactria, and Xinjiang, and were sending periodic raids down into the Gansu corridor then your analogy might make sense. You're right that it's difficult to imagine the logistics of Roman legions accomplishing that kind of feat. On the other hand, the Mongols were already in Europe and had already conquered their way into Russia and Asia Minor. There's really no reason to think long-range logistics should be the limiting factor in, say, Poland, the Hungarian plain, or Vienna when it wasn't for Baghdad or Kyiv. Long-range invasions over thousands of miles aren't easy, but they have been done since the Achaemenids, done over the silk road well into Central Asia since the Han, and done several times by nomadic confederations who appear suddenly from the mongolian steppe and dominate settled peoples. The Mongols were just the latest and the best at it, and Genghis wasn't even alive during the western conquests that could have taken Europe.