Alright, what if Kublai's invasion of Japan was successful at landing, with little loss of troops and supplies by ocean and storm?
How much could the Mongols take? What impact would this have on the Mongol Empire and Japan?
The issues are basically this: The first invasion was too small in its composition of forces, and the second invasion faced an enemy that was now well-prepared.
The first may have only been a raid or an intelligence-gathering exercise. And thus it was comparatively minor affair, so the Mongol leaders don't have much motivation to draw things out. I'm not sure how far the Mongols got: I don't think they actually broke out of Daizaifu in 1274. Therefore, even if they kept fighting and won there, there's still a lot of ground to cover before the 1274 army would reach Kyoto or Kamakura, which are the two most important places in Japan. Even before they withdrew, Mongol forces had failed to score the decisive landing they needed (their conquests of Tsushima and Iki went along fine though), so maybe they'll get tired. Therefore, even if you take out the storm, I think there's the possibility that Mongol forces get overwhelmed by Japanese ones, or they are victorious and choose to leave anyways.