You for got the kennel masters daughter.
Serious nerd answer?
Because its a medieval fantasy based on European folklore and history, and communication with the far east was limited during this period in history.
Weteros is western Europe. The free cities are the Mediterranean. The slaver cities (Mereen, Astapor) are the Middle East/Ottoman Empire. Valyria is Rome.
There are far eastern civilizations on the Planetos, but they are much further east than any character on the show has traveled (For reference, I think Quarth is about halfway there).
The Jade Sea, Yi ti, and Ashai (where the red woman is from) would all be populated with Asians (or the Planetosi equivalent)
FWIW there is a pretty popular fan theory that uses Quaithe's prophecy ("to go West you must go East") as justification for Dany's eventual journey Eastward. There is a potential travel route to the West coast of Westeros via the ocean to the East of Ashai. Ashai also has it's own version of the Long Night legend, leading some to believe that the Others also attack Essos when they return.