The "Oath" is laid out in the Constitution Article 2, Section One, Paragraph 8:
Before he enter on the Execution of his Office, he shall take the following Oath or Affirmation- "I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States.
Its not simply ceremonial, its the Law.
You forgot the 20th Amendment, Section 1.
Power used to transfer at the oath. Now it transfers at noon.