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.