Why do we not want to make it public? Not trolling but really asking this. It could lead us to a better overall system. If people can find out who I voted for and hence I would be in trouble then we have a broader systemic issue. If we can solve that voting can be so much more efficient and more importantly impactful.
Also could we anonymize the voter that way it’s like any other legally private information that can be accessed with a warrant etc.
(I think Brendan Eich's experience with suffering enormous professional consequences for having donated to the Proposition 8 campaign -- a fact which was public under California electoral laws -- is a concrete example. You could imagine the same kind of consequences for everyone who voted for the proposition, in which case many people would not only choose their political donations based on fear of public opinion and social and professional consequences, but would even choose their votes based on those same fears.)
These issues might not convince you, but they represent a sample of other people's answers to your question. Also, in many places, depending a lot on the culture and history, a powerful local figure such as a large employer, union leader, "patron", or religious leader will actively try to tell people how to vote, if given the opportunity.
Verifiable public votes are the one piece missing for a successful "cash for votes" program, which many people (including myself) would consider highly undesirable, and even a perversion of democracy. Over $14B is being spent on the US elections in 2020[1], or more than $40 per US citizen, or nearly $60 per eligible voter. If a campaign or other party could offer citizens $50 in cash in exchange for verifiable proof that the citizen voted in the specified manner (either above the table or... not), that would change the nature of US elections entirely.
Also could we anonymize the voter that way it’s like any other legally private information that can be accessed with a warrant etc.