It may be worth noting that the transition from soldiers taking an oath of loyalty to the state to an oath of loyalty to an individual leader is one of the changes that was important in the fall of the Roman Republic and rise of the imperial system.
During the Republic, military oaths promised fidelity to Rome. As the Republic fell apart, there are some claims that Julius Caesar had his legions swear allegience to him, but there is also some doubt about this.
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https://www.jstor.org/stable/41531205
In the next generation, as Caesars heir Gaius Octavius (Octavian, later Augustus) was slugging it out with rival wannabe heir Marcus Antonius, oaths of loyalty to the general personally were used, and when Octavius became the Emperor Augustus he set the precedent (followed by his successors) of oaths of all legions, not just those he personally commanded, were made not to the state, not to their general, but to the Emperor.
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https://www.jstor.org/stable/707277
During the conflict between Octavius and Antonius, Octavian took this a step further, with a "voluntary" oath from everybody in Italy to support him!
External Quote:
The Oath of Italy (Coniuratio Italiae) was an historical event that took place in 32 BC, by which Italy swore allegiance to Octavian Caesar in the Final war of the Roman Republic against Cleopatra and Mark Antony. Augustus himself retells the facts in the Res Gestae Divi Augusti: "The whole of Italy voluntarily took oath of allegiance to me and demanded me as its leader in the war in which I was victorious at Actium."[1] Following the event, the Western provinces of Sicily, Sardinia, Spain and Gaul also sided with Augustus, and the same happened with the Eastern provinces and Egypt following the conflict. The Oath of Italy was foundational for the birth of the Roman Empire in a similar way that the Oath of Brutus was declared to overthrow the Roman Kingdom, as both were used as an expression of the will of the people.
Source:
https://en.wikipedia.org/wiki/Coniuratio_Italiae
Whether or not the leaders of the current regime in Washington would LIKE the military to do this in relationship to the President seems speculative -- at any rate, they have not attempted to carry out such a plan, to my knowledge. And while it was a part of the process that led to the collapse of the previous world-straddling republic as it transitioned into autocracy, I'm not sure to what extent it was a cause and to what extent effect of that change. Nor would I expect an exact replay of that process in our time, even if we were to be undergoing such a transition (I fear so more some days than others.)