So why did the hook nose "become a thing" in discriminatory appearance?

[Roberto]

The bad guys in the OP image have "demon noses", not "hooked noses". Literally demonizing the enemy.

Well its more the typical jewish nose which also is referred to ask hooked nose. Not sure if this has any relations but considering history does have its roots.
https://en.wikipedia.org/wiki/Jewish_nose


"Jewish nose or Jew's nose[1] is a racial stereotype[2] that refers to a hooked nose with a convex nasal bridge and a downward turn of the tip of the nose[3] that was singled out as a hostile caricature of Jews in mid-13th century in Europe, and has since become a defining element of the Jewish stereotype."