There’s no good answer beyond: tradition.
The folk-history of the instrument holds that it was popularized on Honshuu first by blind beggars - who would have little use for visual markers.
Informal play in folk music settings were less about position and more about playing by ear; it’s only recently that specific arrangements have begun to be written down.
Formal play in the context of kabuki, bunraku, or chamber music often relied upon written scores to be followed which precluded players from looking at their instrument. Stage etiquette also demands that the performers, or jikata, essentially fade into the background. Moving as little as possible and always in unison.
As well, the removable fujaku serves the same purpose - but it’s mostly a crutch for students. As your ears and muscle memory mature it becomes less useful and more distracting.
Aesthetics play a strong role as well. Some players prefer to keep their instruments pristine and let the grain (especially the prized tochi pattern) shine.It should be noted that one may find that the grain and imperfections in the wood can serve the same purpose as painted on markers.
What you see on Ms. Ninagawa’s instrument are hand painted. My tsugaru has them too, although my other instruments do not.