They do take such an oath.
Per Article II, Section One:
The President shall, at stated times, receive for his services, a compensation, which shall neither be increased nor diminished during the period for which he shall have been elected, and he shall not receive within that period any other emolument from the United States, or any of them.Now read the preamble of the Constitution [used as part of the basis for the 1869 SCOTUS Texas V. White decision that the states had no right to secede because they had become part of a *perfect union*] in particuilar the LAST EIGHT WORDS....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."
You say that the Presidents have not taken their oath of office. However, you are wrong. They have taken it.
You imply that the last 8 words of the preamble have some meaning that somehow legitimizes secession.
In reality, the preamble precludes secession, since any attempt to disestablish the Constitution in any part of the Union is not an act of the people of the United States, but an act of an illegitimate party that cannot claim to on behalf of the people of the United States.
"...this Constitution for the United States of America." OK, so?