Gomusin for men were modeled after "gatsin" (갖신), and ones for women were danghye (당혜).
They were much easier to keep clean than danghye and jipsin (straw shoes) and they could be worn when it rains.
[1][2] It is purported that the first man to wear gomusin was Sunjong of Korea, the last emperor of Joseon.
From 1938 to 1945, the Japanese colonial régime restricted the wearing of national dress including gomusin.
This is likely the cause of their decline in popularity: they are relatively heavy and unergonomic, making them uncomfortable to wear for extended periods of time.