Should every American have a secret ballot when voting for a possible next President?

[Boojatta]

In particular, why should judges who are currently on the Supreme Court have a secret ballot? Are we supposed to believe that no judge on the Supreme Court would ever get involved in any official court business that might have partisan political implications?

There are three branches of government. In two of them, candidates either run as independents or have some official party affiliation. Hiding the political affiliation of Supreme Court judges doesn't remove bias. It simply hides bias.

Would it be possible to remove executive and legislative authority over the judicial branch of government and allow for the establishment of parties of interpretation? The legislative branch drafts legislation, so parties of interpretation would not have policy in support of (or in opposition to) any particular laws (except insofar as they could interpret the Constitution as contradicting some proposed laws.) They would have policies with respect to interpretation.