No issue has take place in regards to the president being subpoenaed. There is no precedence. There have been ruling in the past that show the Executive and Legislative Branch's actions have been contradictory to the constitution.
The Executive and the Judicial branches need to have private communications to discuss important information. They a allowed to protect some of these conversation.
Judicial branches cannot full provide justice if not all the information is available to them. This would cause speculation to take place. That is not Justice.
The sixth amendment allows during criminal trial for the accused to be confronted with witnesses, and allowed to obtain witness. The Fifth Amendment that no person shall be deprived of liberty without due process. It is up to the court to protect these rights.