>Interesting take. Worth considering.
Not denigrating the Bible, but in this context it is just a book used symbolically. There is no binding legal requirement that determines any book must be used in these ceremonies.
Article VI Supreme Law
Clause 3 Oaths of Office
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
https://constitution.congress.gov/browse/article-6/clause-3/