I don't think this is the case. All military members of all branches are taught that they must not obey unlawful orders. Killing elected officials is clearly unlawful.
And the president is still subject to impeachment.
Is this not a problem given impeachment votes will follow party lines? A party with the presidency and with >1/3 of the senate would have unchecked power. As long as there are individuals who are willing to execute the orders (who can later be pardoned), the president could delay elections or eliminate political rivals indefinitely. The system of checks and balances were put in place by the founders assuming each party will serve their own interests. Politics aside, if this immunity is given to the president, the current system would provide no checks for the executive branch of a party willing to exercise the full extent of those powers. People would essentially be expecting on good faith each election that the president will not become a dictator; there would be no procedure to actually prevent that.
My concern is the immunity allows for perpetual, single party rule with only a 1/3 of senate seats and the presidency. There would be no checks in place at the federal level if the party was willing to exercise power to interfere with elections or opposing candidates.
It may be unlawful, and it may fail because lower level officers refuse. But it seems like in that case the president cannot be charged. Lower level officers that go along with it could, but the president has the ability to pardon them.
So even if I some case they fail, there are no consequences so people can try again.
Yes there is also political considerations, but if the president feels confident enough to plan assainations of a rival, or for instance a coup with others in the executive branch, then he must feel he has that handled.
And the president is still subject to impeachment.