Why do you think this right is such a critical linchpin of the American judicial system?

Incomplete question. The complete question reads;

According to the text, what is the "central right of the accused"?  Why do you think this right is such a critical linchpin of the American judicial system?

anyone charged with a crime is innocent until proven guilty in court

Explanation:

Because of the believe in due process, that is, following the laws of the constitution equally among every citizen, it has made the right to fair hearing possible so that no one can be prosecuted without been proven guilty of the accused crime.

Remember, the term justice means fair treatment, so this central right of the due process allows for Justice; a principle the American Judicial system stands up for.