Angels wings is so important to them because it's thier source of happiness and everything. Once this is gone. expect that the angel will be in despair and lonely. Once an angel have no wings they tend to abandoned their duties as a guardian of human.

Dwelling in the human world takes courage for them to do. so, once an angel recieved their duties it is not necessary to take it lightly. you will be punised or banned by the lord of the sky.