Targaryens are depicted as famously having violet eyes and silver-blond hair. They got the hair decently right with Daenerys and Viserys, but the producers didn't go for the violet eyes.
Targaryens have violet eyes and silver-blond hair due to their Valyrian roots, as these are the traits of the people of Valyria, according to "A Game of Thrones."
On the other hand, staring at violet eyes on TV could get distracting.