The vid says he was abandoned at birth because of the way he looked??? I'm guessing whomever made that video has never seen a newly hatched budgie before because they're not born with feathers, they're about an inch high and naked. That bird has some kind of feather disease that makes its feathers grow like that.
The mutation happens from time to time in Budgies and breeders will usually cull them. They're usually called Featherdusters but I guess if they're well cared for then there's no problem but I would recommend trying to breed them!
I know that in some hairless breeds of mammals like chinese crested dogs and hairless rats, dental deformities and (I think) nail deformities are more common. I wonder if the featherduster cage birds are prone to odd beak problems or other unexpected issues.
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Because most of them die before they're a year old. It's not just "curly feathers" that make up the phenotype. The feathers basically don't stop growing, and around the age that normal budgies undergo their first molt is usually when these feather dusters die. A very few live on with TLC.