To your first point, John Wayne played best only characters who were depicted as American. Period.
As to your second question, I was deployed to Central Asia and spoke with Uzbeks, Tadjiks, Kyrgyz and Kazakhs. They all admired the region’s greatest conquerors: Aleksandr Makedonskii (the Great), Temujin (Genghis Khan) and Timur the Lame (Tamerlaine).
How these historical figures would have been authentically depicted in film, I don’t know except that an ethnic Central Asian actor would have done better with the latter two than the quintessentially American icon, John Wayne. Yeah, there’s probably no one in the filmmaking capitals of Tashkent or Bishkek with equal star quality.
Casting Genghis Khan as a romantic hero is a bit of a stretch anyway, IMO.