Idk, i think its important to distinguish between side effects that would also happen via diet and exercise vs side effects that do not happen when losing weight via other means.
It sounds more like malnutrition and starvation.
I'll concede it may still be better than being fat, though.
That said, based on googling telogen effluvium seems to have lots of causes not related to malnutrition, even if insufficient protein is one of the causes.