The public policy purpose is to allow independent verification of who voted, in furtherance of trust in elections. It is arguably one of the reasons voter fraud is extremely rare in U.S. elections. “Many eyes make bugs shallow,” to steal a phrase.

Unfortunately, a lot of people still believe in widespread voter fraud despite the obvious and well-documented rarity.

I would say something similar about the availability of voter files, though. A lot of people are horrified they are available despite the obvious and well-documented lack of evidence it causes any significant harm.