It's a matter of dynastic longevity and volume of surviving sources.

The Koryŏ dynasty ruled from 918 to 1392, and the Chosŏn from 1392 to 1910. So if you want your story set at any point in the thousand years from 918 to 1910, it must be set in one of those two eras.

The Koryŏ and Chosŏn were the two most recent eras in premodern Korean history, and the historical documentation for those two is simply overwhelming compared to earlier periods. Consider the "orthodox histories" (chŏng sa), an East Asian historiographical genre referring to a series of authoritative histories compiled by an army of state-funded historians (e.g. China's Twenty-Four Histories). For narrative historians of Korea, and hence for popular media creators, the chŏng sa are usually unparalleled in volume and reliability.

The main official histories of Korea are:

• Historical Records of the Three Kingdoms, or Samguk Sagi. The official history for 57 BC to 936 AD. Approximately 192,000 Chinese characters.

• History of Koryŏ, or Koryŏ Sa. The official history for 918 to 1392. Approximately 3,370,000 characters.

• Veritable Records of Chosŏn, or Chosŏn Sillok. Length: Approximately 49,650,000 characters.

Not to mention that while very little in the way of narrative history survives outside the chŏng sa for the Three Kingdoms period, and things are similar, if not quite as dire, for the Koryŏ too, the sheer volume of preserved Chosŏn-era documents is staggering in both volume and variety of genres.

So there's simply far, far, far, far more material to make TV shows about for the Koryŏ and especially for the Chosŏn than for any earlier era in Korean history.