Yi Sun-sin became a coalition symbol of victory

Did Yi Sun-sin's death damage morale beyond the Korean navy?

Yes. His reputation had become a coalition-wide symbol of victory, so Chinese as well as Korean forces felt the loss.

Yi's death shook more than the Joseon fleet. By the end of the war, allied Chinese forces also treated him as a token of expected success. Napoleon provides a comparison for the confidence that a celebrated commander could add merely by being present with an army. Yi's reputation had multiplied his practical influence across a coalition while his direct value as a commander remained important.