Because biliary atresia is going to block more than just conjugated bilirubin excretion; you are going to have no cholesterol excretion, no bile acid/salt excretion, no toxin secretion -- nothing.
Dubin-johnson is just a defunct transporter for your conjugated bilirubin, which is water soluble and can be excreted in your urine relatively harm-free.
Because biliary atresia is going to block more than just conjugated bilirubin excretion; you are going to have no cholesterol excretion, no bile acid/salt excretion, no toxin secretion -- nothing.
Long answer: Ductular reaction. Damage to the blocked biliary ducts causes inflammation and reactive ductule formation along with fibrosis. A very interesting article outlines why Alagille syndrome, which also has ductopenia and cholestasis rarely progresses to cirrhosis.